Charlton, a World Cup winner with England and one of United's greatest players, died on Oct. 21 at the age of 86.
Former United manager Alex Ferguson, former players Andy Cole and Paul Scholes, England manager Gareth Southgate, and Prince William were some of the early arrivals among the some-1,000 invited guests at the cathedral for the service.
A throng of fans a dozen deep in places braved the blustery weather to clap as the cortege made its way in front of the Trinity Statue of Charlton, George Best and Denis Law, where a rings of hundreds of bouquets and scarves encircling the statue's base continues to grow.
Charlton was a key figure in England's 1966 World Cup-winning team, playing alongside his brother Jack. He made 758 appearances for United, scoring 249 goals.
Harry Maguire, Jonny Evans, Tom Heaton and Luke Shaw were among the current United players scheduled to attend the private service, with many absent due to international duties. Current manager Erik ten Hag was not able to attend due to a commitment in the Netherlands.
The ceremony was expected to include tributes and eulogies from United chief executive David Gill, former Manchester United Foundation chief executive John Shiels and a personal tribute from Charlton's family.
Hymns were to include Abide With Me, which is traditionally sung before the FA Cup final.
The England team's arrival at their training base at St. George's Park was delayed on Monday to allow Southgate, Maguire and others to attend.
"Arguably we are talking about the greatest English footballer we have ever had," former United captain Steve Bruce told Sky Sports. "Then of course, he had class as a man too. So when you have the mixture of the two you can understand why there are going to be thousands of people lining the streets.
"One simple thing he always said (when I joined United), 'It's a great club. Just enjoy it, enjoy the privilege of playing for this great football club.'"
Another former United captain Bryan Robson called it a "sad day for football, for Man United and Sir Bobby's family".
"He was a fantastic player, but not just that, he was a great person," Robson told Sky News.
Charlton was a key figure in England's 1966 World Cup-winning team, playing alongside his brother Jack. He made 758 appearances for United, scoring 249 goals, winning three league titles, the FA Cup and European Cup.
