Wins for Scotland, Serbia, Sweden, Switzerland and Ukraine moved each closer to at least a place in the playoffs next year with the finals tournament in Qatar in sight.
The 21-year-old Sancho moved to United from Borussia Dortmund in the offseason for $100 million.
Raheem Sterling, Harry Kane and Harry Maguire scored in a 14-minute flurry and Declan Rice added a fourth second-half goal.
'Bring it home': Queen Elizabeth II, Prince William wish England football team success ahead of Euro final
Prince William, the President of England's Football Association (FA), on Sunday released a video message wishing the squad led by captain Harry Kane the "very best of luck for tonight".
Maguire was a major doubt for the European Championship, but Gareth Southgate waited on him even though the former Leicester defender was not fit until the third group game.
It marked the first time that England scored four goals in the knockout stage of a major tournament since beating West Germany 4-2 in the 1966 World Cup final.
AS Roma coach Jose Mourinho has said England should be able to reach the finals of the ongoing Euro 2020.
England managed to progress to the round of 16 stage after finishing the Group D toppers following a win over Croatia and the Czech Republic.
Southgate has restored the reputation of the England national team from the lows of a humiliating Euro 2016 exit against Iceland in the round of 16 and the ignominy of Sam Allardyce's brief tenure.
At the European Championship, it's meant the playing availability of Mount and Chilwell is more in the hands of the Public Health England government agency than national team coach Gareth Southgate.
The Scottish sides of 1967 and 1977 are still fondly remembered for victories at Wembley in the old British Home Championship.
Gareth Southgate's lack of a stellar coaching CV at club level has counted against him in the eyes of his doubters.
The 28-year-old central defender has not played since injuring ankle ligaments in Manchester United's Premier League defeat by Aston Villa on May 9.
Perhaps Harry Kane is the only certain starter, with Raheem Sterling, Jadon Sancho, Jack Grealish and Phil Foden vying for roles.
The final warmup match before Euro 2020 — against Romania on Sunday — is also being played in the northeast town of Middlesbrough.