“English Terrace Row” (or “Renwick Row”) in Manhattan is located on West 10th Street, between Fifth Avenue and Sixth Avenue (Avenue of the Americas). The row of houses was designed by James Renwick Jr. (1818-1895) and built between 1855 and 1856. The houses abandon the high Dutch “stoop” (step) and have entrances that are level with the street.
   
“‘The English Terrace’ Row” name was published in the AIA Guide to New York City (1968). “10 ST. West between 5th & 6th. Converted townhouse on Renwick Row” was printed in a classified advertisement in the New York (NY) Times on December 27, 1970.
                 
   
Wikipedia: James Renwick Jr.
James Renwick Jr. (November 11, 1818, Bloomingdale, in upper Manhattan, New York City – June 23, 1895, New York City) was an American architect in the 19th century. The Encyclopedia of American Architecture calls him “one of the most successful American architects of his time”.
   
GOogle Books
AIA Guide to New York City
By Norval White and Elliot Willensky (American Institute of Architects. New York Chapter)
New York, NY: Macmillan
1968
Pg. 60:
“The English Terrace” Row, 20-40 W. 10th St., bet. Fifth and Sixth Aves. S side. 1855-1856.
These were the first group of row houses in the city to abandon the high, Dutch “stoop” (which is Dutch for step), making the entry floor only two or three steps up from the street. Being the first builders in Nieuw Amsterdam, they followed the home style: high stoops way off the canal or street to protect the basement from periodic flooding—despite no threat from the local waters. “Terrace” does not refer to the handsome balcony that runs the length of these houses; it is the English term for a row of houses, such as are found in the Kensington and Paddington districts of London of the 1840s, 1850s, and 1860s.
 
27 December 1970, New York (NY) Times, sec. 8, pg. 3, col. 1 classified ad:
10 ST. West between 5th & 6th. Converted townhouse on Renwick Row. 5 room - garden duplex plus office for buyer, $53,000 cash over PM mortgage. Ely-Cruikshank Co., Inc., 150 W. 10 St., Village Office, 349-8335.
 
26 August 1979, New York (NY) Times, “Chelsea Town House Revival Widens” by Carter B. Horsley, sec. 8, pg. 1, col. 2:
One Manhattan exception is the “English Terrace” row on Tenth Street between Fifth Avenue and the Avenue of the Americas that has been attributed to James Renwick Jr., the architect of St. Patrick’s Cathedral and Grace Church.
     
Google Books
I Love New York Guide
By Marilyn J. Appleberg
New York, NY: Collier Books; London: Collier Macmillan Publishers
1988
Pg. 43:
English Terrace Row
20-38 West 10 Street between Fifth & Sixth Avenues. (James Renwick, Jr., 1856-58.) Modeled after England’s row houses. abandoning the high Dutch stoop. On a lovely Greenwich Village street.
   
Google Books
Architectural Guidebook to New York City
By Francis Morrone
Layton, UT: Gibbs Smith
2002
Pg. 81:
10TH STREET
From Sixth Avenue to Broadway
One of the most interesting streets in the Village. It has a little of everything, all harmoniously related and surpassingly urbane. Numbers 20 to 38, between Fifth and Sixth avenues, are known as “The English Terrace Row.” Built in 1855-56 and attributed to James Renwick, Jr., architect of Grace Church (6.9) and St. Patrick’s Cathedral (13.8), these ten severe Italianate facades are unified by a balcony that stretches continuously along the row above the ground story. This was also the first level of houses in the city to place its entrances on street level, abandoning the high Dutch stoop.
 
New York (NY) Sun
Communal Balconies as Urban Verandas
In The Details ...
By CARTER B. HORSLEY, Special to the Sun | July 31, 2008
(...)
The most attractive example in Manhattan is the English Terrace Row, designed by the architect of St. Patrick’s Cathedral, James Renwick Jr., at Grace Church on Broadway at 10th Street. The English Terrace Row was built between 1856 and 1858 and consists of nine brownstones at 20-38 W. 10th St. Neighbors often festoon the ornate cast-iron communal balcony on the second floor with lights at Christmastime.
     
Off the Grid (Greenwich Village Society for Historic Preservation)
A Glimpse of the Gilded Age on Renwick Row
BY SARAH BEAN APMANN – JULY 20, 2017
(...)
Located on the south side of West 10th Street between Fifth and Sixth Avenues, this row or “terrace” of ten houses at #20-38 was built in 1856 (with the exception of No 38, built in 1858) in the Anglo-Italianate style.  Their design is attributed to American architect James Renwick, Jr. (1818-1895), considered one of the preeminent 19th century American architects.  Best known for his designs of St. Patrick’s Cathedral and Grace Episcopal Church in New York City and the Smithsonian Building in Washington D.C., Renwick was trained as an engineer and received his bachelors and masters degrees from Columbia College, first matriculating at the age of 12.  In addition to the row on West 10th Street, the Anglo-Italianate houses at Nos. 23-35 Stuyvesant Street and Nos. 114-128 East 10th Street, also known as Renwick Triangle, are also attributed to the architect.  These two groups of row houses are believed to be the only extant rows by Renwick in New York City.
 
Ephemeral New York
The beauty of 10th Street’s English Terrace Row
October 16, 2017
Shared balconies stretching across several buildings in a row aren’t the norm in New York City.
 
But a graceful cast-iron communal balcony ties together the brownstones at numbers 20 to 38 West 10th Street. It’s one of the many features that make what used to be called “English Terrace Row” on this Greenwich Village block so harmoniously beautiful.
 
English Terrace Row, known these days as Renwick Row, was built between 1856 and 1858 by James Renwick Jr., the architect behind circa-1846 Grace Church three blocks east down 10th Street.