The ‘andante’ dating to 1924 was notated on musical manuscript and then signed by the great composer - who was also a Wolves fan.
He regularly cycled to matches from his home in Great Malvern, Worcestershire, and wrote what is believed to be the world’s first football anthem, He Banged The Leather For Goal.
The manuscript featured in Richard Winterton’s Library Sale at The Lichfield Auction Centre, Fradley Park, Staffordshire, on Tuesday
Mr Winterton – auctioneer of BBC Bargain Hunt and Dickinson’s Real Deal – discovered the music paper tucked inside an autograph book, with signatures dated to 1923 and 1924.
The manuscript sold to a private buyer in London for £5,400, and the autograph book went for £3,600 to a private buyer in the Midlands.
Auctioneer Richard Winterton said: “The excitement built. With more than 1,000 watching it online and 35 registered bidders on this lot at any one time, plus bidders on the telephones and a packed room, it just showed what an incredible find this was.
“And the vendors were in the room, which put extra pressure on!
“We are absolutely delighted with these results – a very well-deserved total hammer price of £9,000 for the manuscript and the autograph book.”
He added: “We understand that the purchaser intends to make the manuscript available to Elgar scholars in case anyone wants to examine it musically. The manuscript will initially be in Winchester and people will have access in due course.”
The new owner of the manuscript, who did not want to be named, said: "One of the great fun things about Elgar at this stage of his life was he was a practical joker and setter of cryptic puzzles on an industrial scale!
“It’s highly likely that if he was to give an unpublished, heroic theme to anybody he would have done it to cause chaos! It would not have been a casual throwaway – that is practically unthinkable. It would be another Elgar cryptic timebomb.”
The items were all collected by Lydia Tabb, a matron at Barnardos, during her time fundraising for the charity.
Relatively little is known about Lydia – at one point she possibly lived in Chertsey, her maiden name was Probyn and in 1939 she married Herbert Edward Tabb, who was described in a contemporary newspaper wedding report as assistant superintendent at the school of handicrafts.
Lydia, who was born in 1897 and died in 1983, worked for Barnardos and at one point travelled to Australia on behalf of the charity.
She also had links to Godalming in Surrey but in her later years lived in a flat at Gravelly Hill, Birmingham.
Sir Edward William Elgar (June 2 1857 – February 23 1934) is regarded as one of England’s greatest composers, with many of his compositions featuring in classical concert repertoires all over the world.