Emma Raducanu, Katie Boulter, Sonay Kartal, Jack Draper, Cameron Norrie and Jacob Fearnley all qualified for the main draw as Britain’s top three women’s and men’s players.
They were joined by Francesca Jones, who came through qualifying, and Billy Harris, who lost in the final round of qualifying but reached the main draw as a lucky loser.
Raducanu was the only British woman to get through the first round but exited in the third round in a brutal straight-set defeat by former Wimbledon champion Elena Rybakina.
Draper also beat a qualifier in Federico Gomez but ultimately withdrew from the tournament with an arm injury, while Norrie was beaten in the third round by Djokovic.
Kartal took 18th seed Beatriz Haddad Maia to three sets before bowing out, while Boulter lost to 27th seed Marta Kostyuk, and Jones was beaten by Eva Lys.
Harris lost in three tight sets on his US Open main-draw debut against 25th seed Felix Auger-Aliassime.