The ‘andante’ dating to 1924 was notated on musical manuscript and then signed by the composer.
Believed to be scored for a string quartet, the tune could be a brief overture for a more comprehensive piece.
It has now been heard for the first time in more than 100 years after pianists Heather Broome and Tony Slater played the piece after transcribing it for piano.
The manuscript will be offered at Richard Winterton’s Library sale on March 26 in Fradley Park, Lichfield, with an estimate in the region of £1000.
The autograph book it was found in had been collected by Lydia Tabb (1897-1983), a matron and fundraiser for the children’s charity Barnardo’s who died in 1983.
Tabb had lived in Surrey and in her later years in Birmingham, and her great-nieces Linda Brewer and Jane Coombs remember visiting her there as children.
Brewer said: “My dad would mow the lawn while we would sit with her eating sandwiches… It’s a bit of a mystery as to how Lydia compiled the signatures of so many famous and influential people and we would love to find out more.”
The autograph album dates from 1923 and contains about 69 signatures including five prime ministers and authors such as Sir Arthur Conan Doyle, HG Wells, Sir JM Barrie and Rudyard Kipling.
The Elgar manuscript and the autograph collection are being sold as two separate lots.
Sir Edward William Elgar (1857-1934) is regarded as one of England’s greatest composers, with many of his compositions featuring in classical concert repertoires all over the world.
Last year a disputed Elgar manuscript that appeared on the BBC’s Antiques Roadshow was due to go on show in British Library.