I've seen the question of which U.S. city has weather most similar to London (which is relevant because a lot of U.S. fashion, particularly formal business clothing, is derived from London norms) discussed often, but rarely with empirical evidence.
The short answer is Seattle, Washington.
In London, the average high temperature in July is 72 degrees Fahrenheit and 45 degrees Fahrenheit in January. It has 164 days of precipitation per year (45%), and 29.68 inches of precipitation per year.
The U.S. Data (from the National Climtatic Data Center, DESDIS, NOAA, U.S. Department of Commerce via the 2016 World Almanac mostly based upon 1981-2010 data).
* U.S. cities that are similarly cool in July (+/- 7 degrees) include:
Anchorage, Alaska (65), Los Angeles, California (74), San Francisco, California (72), Caribou, Maine (76), Portland, Maine (79), Sault Saint Marie, Michigan (76), Duluth, Minnesota (76), and Seattle, Washington (76).
* U.S. cities that are similarly warm in January (+/- 7 degrees) include:
North Little Rock, Arkansas (50), Denver, Colorado (44), Wilmington, Delaware (40), Washington D.C. (43), Atlanta, Georgia (52), Boise, Idaho (38), Dodge City, Kansas (44), Louisville, Kentucky (43), Baltimore, Maryland (41), Kansas City, Missouri (38), St. Louis, Missouri (40), Reno, Nevada (46), Atlantic City, New Jersey (42), Albuquerque, New Mexico (47), New York City, New York (38), Raleigh, North Carolina (51), Oklahoma City, Oklahoma (50), Portland, Oregon (47), Philadelphia, Pennsylvania (40), Memphis, Tennessee (50), Nashville, Tennessee (47), Norfolk Virginia (48), Richmond, Virginia (47), Seattle, Washington (47), and Charleston, West Virginia (43).
* U.S. cities with similar amounts of precipitation per year (+/- 8 inches a year) include:
Chicago, Illinois (36.89), Des Moines, Iowa (36.01), Detroit, Michigan (33.47), Sault Saint Marie, Michigan (32.95), Duluth, Michigan (30.96), Minneapolis, Minnesota (30.61), Omaha, Nebraska (30.62), Oklahoma City, Oklahoma (36.52), Portland, Oregon (36.03), Dallas, Texas (36.14), Burlington, Vermont (36.82), Seattle, Washington (37.49), and Milwaukee, Wisconsin (34.76).
* U.S. cities with similar numbers of days of precipitation per year (+/- 16 days a year) include:
Buffalo, New York (173), Burlington, Vermont (155), Caribou, Maine (165), Cleveland, Ohio (178), Grand Rapids, Michigan (168), Pittsburg, Pennsylvania (148), Portland, Oregon (158), and Seattle, Washington (150).
There is exactly one city which is on all four lists: Seattle, Washington which is four degrees warmer in the summer and two degrees warmer in the winter. It gets a 7.81 inches more precipitation per year than London but on 14 fewer days. No other city is on both the January and the July temperature lists. The slightly warmer January temperatures in Seattle, however, mean that Seattle gets much less snow than London whose average low temperature in January is 32 degrees Fahrenheit.
Elsewhere in North America, Vancouver, British Columbia is a very close match to London in temperature with average January high (44), average July high (72), and in number of days of precipitation per year (165), but has about 50% more total precipitation per year (45.4 inches) (per Wikipedia).
All other American cities have hotter summers, colder winters or both.
Burlington, Vermont and Portland, Oregon have similar precipitation to London, and Portland, Oregon also has mild winters, but Portland's July high temperature averages 81, quite a bit warmer than London in the summer. Burlington is as warm as Portland, Oregon in the summer, and has much cooler average highs (27) in the winter.
Sault Saint Marie has mild summers, similar amounts of precipitation, more days of precipitation (181), but much colder January average highs (23). Duluth has fewer days of precipitation (137) and much, much colder January average highs (19). Portland, Maine has cooler January average highs (31), more precipitation per year (47.25 inches), and fewer days of precipitation (136).
San Francisco (20.65 inches from 54 days of precipitation a year) is considerably drier than London and has somewhat warmer January average highs (56) but earns honorable mention for the seasonal morning fogs that it, like Seattle, shares with London.