“London broil” was popularized by New York City restaurants in the 1920s-1940s; the term “London broil” is seldom used in London, England. It is possible that a New York restaurant or club added “London” to the name to make the meat dish sound more expensive and sophisticated.
 
London broil originally was flank steak, but top round roast is used today. The meat is cut in thin strips, against the grain (at a 45-degree angle). “London broil” is sometimes advertised as a specific cut of beef, but there is no such thing. “London broil” is a cooking method (broiling) and a preparation method (slicing against the grain).
 
There is one known, isolated citation for “London broil” in 1902; print citations become more numerous in the 1920s and 1930s.
 
 
Wikipedia: London Broil
London Broil is a beef-based food dish usually made by broiling or grilling marinated flank or round steak and then cutting it against the grain into thin strips.
 
Although many butchers will label a cut of meat “London Broil”, the term does not refer to a specific cut. The cut of meat traditionally used is flank steak, but top round roast/steak is also commonly used. Because the muscle fibers run the entire length of these cuts, the meat can be tough if not tenderized via pounding or massaging. Scoring, stabbing, cutting, penetrating, or otherwise mutilating the cut before sending it into the broiler will ruin an expensive piece of beef by letting all the desirable juices run out of the meat into the pan.
 
The preparation of London Broil typically involves marinating the meat for several hours followed by heating in an oven broiler or outdoor grill. In both heating methods the meat is placed approximately three inches from a direct heat source and turned several times to promote even cooking and avoid burning. It is commonly served in thin slices, cut across the grain.
 
In Canada a ground meat patty wrapped in flank or round steak is known as a London Broil. Some butchers will wrap the flank steak around a concoction of seasoned and ground or tenderized flank steak (Zehrs Grocers in the GTA). Others sell a pork sausage patty wrapped in flank or top round steak labeled as London Broil (Goeman’s Lakeshore Meats in St. Catharines, Ontario, Canada). The website for Goeman’s differentiates between Canadian London Broil (the sausage patties wrapped in Top Round Steak) and American London Broil (Top Round Steak). Another variant, popularized in Ontario, is a London Broil “loaf”, wherein the tenderized flank steak exterior is wrapped around minced and spiced veal as the filler. In some regions, bacon will be added between the flank steak and the veal grind.
 
Ask the Meatman
London Broil
Let’s get it straight, London Broil is a Cooking Method -
NOT a cut of beef!!
But, many grocery store meat departments and butcher shops sell a cut of beef labeled London Broil. 
What cut of beef is it usually?
It is usually Top Round Roast.
(...)
To the right is a rough diagram of how to cut the top round steak after cooking at a 45 degree angle across the grain.
 
Sometimes it is stated before cooking to score the beef cut in a diamond pattern
 
That’s basically it.  It is not a very unusual cooking method.  The recipe first appeared in print in the U.S. in the early 1930’s, and consisted of marinated flank steak.
Today the recipe more often calls for a Top Round Steak (or Top Round Roast).
     
About.com: Barbecues & Grilling
London Broil
If you think you know what this is, you’re probably wrong
By Derrick Riches, About.com
London Broil, despite what you might find at the local meat market is not a cut of beef but rather a method of cooking. It was one of the first recipes to become popular in early restaurants and so the name London Broil because synonymous with a cut of meat. Originally that cut of meat was flank steak, but over the years the name has been applied to almost any cut of beef that is very lean and less tender. Hence you might find London Broil being a steak or a roast that comes from the sirloin or round sections of cattle. This of course makes the whole thing very confusing.
 
To make matters worse the original method of the London Broil was simply a flank steak, pan fried to medium rare, cut cross grain and served. This method is perfect for a flank steak because it becomes very tough if cooked too long and by cutting it into strips you made it easy for even the dullest of teeth to get through. (...)
   
Ochef.com
What is London Broil and How do I Grill it?
Q. Will you tell me how to grill London broil?
A. Yes and no. If your grocer has labeled the cut of meat you have as London broil, skip to the next paragraph. To purists, London broil is a preparation, not a cut of meat. It is a steak that is pan-fried (and therefore not grilled) over high heat only to medium rare, beyond which point it becomes inedibly tough. It is a useful preparation for lean, tough cuts of meat, such as flank steak, shoulder, and round. To the less pure, London broil is a preparation that involves marinating a flank steak, then grilling, broiling, or pan-frying it.
 
Some absolutely promiscuous butchers label various cuts of meat London broil, including flank steak, sirloin tip, top round, etc. We’ll assume you have a flank steak. For best results, marinate the meat for several hours or overnight in the refrigerator in the marinade of your choosing. (...)
 
Cooks.com
LONDON BROIL  
12 ounces red wine
1/4 cup water
3 tablespoons ginger
4 tablespoons garlic, minced
1 teaspoon parsley
2 pinches oregano
1 bay leaf
1 London broil steak
Mix all ingredients together in a dish large enough to cover the meat.
Refrigerator and let marinate overnight.
 
THE NEXT DAY:
Preheat oven to 400°F.
Position steak about 6 inches from broiler. Broil until the top side is browned, flip, and pour some of the remaining marinade on the other side.
Do the same for the other side until it is cooked to your taste.
Score steak diagonally using slices about 1 cm thick.
   
Cooks.com
GRILLED LONDON BROIL  
1 london broil, 2-4 lbs trimmed
1 bottle red wine
ground black pepper
meat tenderizer
 
For a lean steak entree, take one London Broil that has been trimmed of excess fat. Place meat in a glass/Pyrex cooking dish, deep enough to accommodate meat and marinade and poke liberally with a dinner fork or score with a sharp knife. Pour enough red wine over meat to cover it, place a towel or cheese cloth over and refrigerate for at least 4 hours, (the longer the better).
 
Remove meat from marinade, discarding liquid, season with ground black pepper and tenderizer and place on grill until done to your liking. One London Broil will usually serve up to four people. Serve over rice or with grilled/baked potatoes and salad.
     
Merriam-Webster Dictionary
Main Entry: Lon·don broil
Pronunciation: \ˈlən-dən-\
Function: noun
Etymology: London, England
Date: 1902
: a boneless cut of beef (as from the shoulder or flank) usually served sliced diagonally across the grain
 
(Oxford English Dictionary)
London broil U.S. (see quot. 1969)
1969 R. & D. DE SOLA Dict. Cooking 143/1 *London broil, large flank steak broiled, then cut in thin slices diagonally across the grain for serving.
1973 E.-J. BAHR Nice Neighbourhood ii. 24 We cooked a London broil out on the grill and ate on the patio.
1974 Columbia (S. Carolina) Record 24 Apr. 14-B/1 Most steak buffs have their favorite cut, and this brings up something I haven’t been able to figure out: the names they give steaks. I’m told that Britons had never heard of London broil until some Yank informed them what it was.
   
What’s What
At Home an Abroad
By F. Sturgis Allen
New York, NY: The Bradley-White Co.
1902
Pg. 41:
London broil.  A false fillet (piece under the kidney) rare broiled.
     
26 June 1922, Bridgeport (CT) Telegram, “Their Married Life” by May Christie, pg. 11, col. 8:
Then she remembered seeing on a restaurant menu something called a London broil.
 
Google News Archive
11 April 1930, St. Petersburg (FL) Evening Independent, “Roast Beef For Small Family Inexpensive By Right Method,” pg. 8, cols. 4-5:
Do not turn the roast in cooking and do not cook it overmuch. In this way you can leave one side fairly rare for the second day. The second day make slices of the roast, fairly thick—one for each one to be served—and broil them quickly—in a gas broiler or over coals. if there is any thickened gravy left from the day before this should be reheated. This is known as “London broil,” and is regarded as a delicacy in clubs and hotels.
 
While you are making ready your slices for the “London broil,” cut up the remainder of the meat, discarding gristle and fatty pieces and putting the good meat through a meat grinder. Simmer the discarded pieces to make soup stock. When it has cooled take off the fat, clarify it and use it for frying. The stock remaining may of course be used as the foundation for soup.
 
The Woman’s World Cook Book
by Lily Haxworth Wallace
Chicago, IL: Reilly & Lee Co.
1931
Pg. 290:
London Broil
A “London Broil” is prepared from a thin flank steak, trimmed, then thoroughly pounded with a wooden mallet or rolling pin to break the long fibers of the meat. A very little flour may be spread over surface of meat before pounding. Broil quickly, season with butter, salt and pepper or spread with Maitre d’Hotel Sauce and cut into thin slices with a slanting motion of knife to cut through as many fibers of meat as possible. Being rather dry, this steak must be very carefully cooked and seasoned, especially in regard to butter.
 
Manhattan Oases:
New York’s 1932 Speak-easies,
With a Gentleman’s Guide to Bars and Beverages
By Gordan Kahn and Al Hirschfeld
With an introduction by Heywood Broun
New York, NY: E. P. Dutton & Co., Inc.
1932
Pg. 62 (“Sam’s”): 
The cuisine is exceptionally good—for the Village. The London broil is especially commendable.
 
15 April 1934, New York (NY) Herald Tribune, pg. 17, cols. 3-4:
London Broil
1 leftover rare roast of beef
2 tablespoons butter
Salt an pepper
Parsley or watercress
Carve the roast into six 1/4-inch slices. Place in a hot skillet in which the butter has been melted. Sear each slice, not allowing more than 1/2 minute to a side. Sprinkle with salt and pepper. Place on a hot platter, garnish with parsley or watercress and serve immediately. This makes 8 servings.
 
1 November 1934, New York (NY) Times, pg. 24 ad:
London Broil
(Gallagher’s, 52nd Street, Just West of Broadway—ed.)
 
7 April 1955, New York (NY) Times, “Recipe for London Broil Offered,” pg. 32:
LONDON BROIL
1 two-pound, high-quality flank steak
1 clove garlic
Salad oil
Melted butter.
1. Preheat the broiler oven.
2. Peel the garlic and cut in half. Rub both sides of steak with galric. Brush steak with salad oil.
3. Place steak on a broiler rack one and one-half to two inches below the heat source. Broil five minutes. Season. Turn steak and broil five minutes. Season.
4. Place steak on plank or platter. Cover with butter. Serve at once. To carve, cut in very thin slices diagonally across the grain. Yield: four to six servings.
 
4 December 1957, New York (NY) Times, “News of Food: Versatile Flank Steak” by June Owen, pg. 63:
To Make London Broil Top Quality Meat Is Required
To Braise in Red Wine Meat Can Be Lean and Less Thick
(...)
Restaurateurs cut London broil on the diagonal for two reasons: First, the steak is comparatively thin. Hence, to get good-sized portions it is necessary to cut the meat on a slant. Secondly, the diagonal cutting severs the connective tissued of the meat which tend to striginess even in choice and prime beef.
LONDON BROIL
1 two-pound, top-quality flank steak
1 clove garlic, halved
2 tablespoons Kitchen Bouquet Charcoal salt, if desired, or salt and pepper
1/4 cup melted butter. (...)
 
17 November 1960, New York (NY) Times, pg. 42:
Flank Steak Cut on Bias Makes a London Broil