Wembley is set to host seven Euro 2020 games, five of which — including the semi-finals and final — come after all Covid restrictions are potentially lifted on June 21.
Wimbledon, which was cancelled last year because of the pandemic, starts a week later, while Twickenham is likely to play a central role to the Lions tour if it is relocated to Britain from South Africa, with the first Test currently scheduled for July 24.
In addition, as many as 10,000 fans could be in attendance at Wembley for the FA Cup Final in May and more than double that for England's group game against Scotland at the Euros.
This morning, Mayor Khan told Standard Sport: "There is finally some light at the end of the tunnel and it would be fantastic if sporting events this summer, including the Uefa men's Euros and Wimbledon, can act as a springboard to recovery for our great city.
"London is the sporting capital of the world — and the best thing Londoners can do is stick to the rules so that we can hopefully make this a sporting summer that lives long in the memory."
Any lifting of restrictions would come too soon for the heavyweight unification fight between Anthony Joshua and Tyson Fury due to take place in London and scheduled for the first week in June.
But promoter Frank Warren said the announcement had boosted the chances of Wembley hosting the second leg of the pair's double-header at the end of the year.
Warren said a capacity crowd at Wembley — some 90,000 people — would still be needed for the fight to go ahead on English soil. "Who knows what's going to happen but, by the autumn, hopefully we'll get back to some normality," he said. "Fight two could very much wind up at Wembley."
British Athletics are hopeful of sizeable numbers — potentially as many as 50,000 — for the Anniversary Games, which will take place at the London Stadium on July 13. The Games will provide a potential final chance for a host of Britain's best athletes to compete prior to travelling to Tokyo for the Olympics.
Wimbledon chiefs, meanwhile, said they were working on every eventuality for the event taking place. In a statement, organisers said: "We remain focused on developing our plans within the scenarios of full, reduced or no public capacity so that we can remain as agile and flexible as possible to the Government and public health situation."
Yesterday's Government announcement has paved the way for the last round of Premier League matches to be held in front of a reduced number of spectators.
The Premier League expect to be guided by clubs on whether to go ahead with any spectators at all, because of concerns about home advantage in any potential crucial final ties, with Fulham hosting Newcastle at Craven Cottage — a possible relegation battle for both clubs.