Ten of the 11 home players in action lost their first-round matches on Monday, with 26th seed and British number one Norrie dumped out 7-6(7) 2-6 7-6(2) 3-6 6-7(4-10) by American qualifier Michael Zheng.
Zheng had five match points in the final tiebreak, after a gruelling four hours on court, but needed only one.
"It always stinks to lose, especially at Wimbledon, my favourite tournament in the world, a tournament I always play so well at," said Norrie, a quarter-finalist last year.
With now-retired Grand Slam winner Andy Murray no longer a saviour in waiting, Britain licked its wounds after losing the most players on an opening day in more than 20 years.
Former world number four Draper had earlier announced his no-show due to an arm injury while fans queuing at the gates knew that Raducanu would not be appearing after she posted an explanatory message on social media on Sunday.
"There have been a lot of painful moments in the last 12 months but this one is definitely the absolute worst," said Draper, who had been due to play big-serving American world number seven Taylor Fritz on Tuesday.
The Briton had told reporters on Sunday that the number of injuries in men's tennis was a concern and tournaments would suffer if something was not done about it.
Former U.S. Open champion Raducanu, 23, withdrew on medical advice as a result of a stress fracture in her right leg.
In her absence, compatriot Harriet Dart opened the play on Court One against Latvia's 2017 French Open champion Jelena Ostapenko.
Dart put up a brave fight over 2-1/2 hours before going down 6-3 3-6 6-4 to an opponent who served more double faults than aces in the first set.
"I'm probably not the one who you wanted to win but anyway thank you, it was a really nice atmosphere," said Ostapenko, whose scowls and grimaces during the match were replaced with smiles of relief after having to work for every point.
Other early British casualties were 17-year-old Mika Stojsavljevic, who lost 6-2 6-1 to Swiss 11th seed and 2025 semi-finalist Belinda Bencic, and Max Basing who went out 6-3 6-0 6-0 to Japanese fellow qualifier Shintaro Mochizuki.
Wildcard Felix Gill lost 6-3 6-3 7-5 to 19-year-old Spanish debutant Rafa Jodar, the 23rd seed, while wildcard Alicia Dudeney was beaten 6-3 6-3 by American Alycia Parks.
They were followed out by Francesca Jones, beaten 6-4 6-4 by Frenchwoman Diane Parry, Mimi Xu and Hannah Klugman -- losing to Daria Kasatkina and 2024 women's singles champion Barbora Krejcikova respectively.
Oliver Tarvet lost to France's Arthur Rinderknech in four sets but Jack Pinnington Jones hung on for another day when bad light ended play with the Briton two sets down and 4-3 behind in the third to American Brandon Nakashima.