Artist Halliwell killed his partner, playwright Orton, in 1967 and then committed suicide.
Orton rose to fame in the five years before his death and in recent years Halliwell’s art has enjoyed a growing following.
Northamptonshire auctioneers JP Humbert will sell a four-panel screen decorated by a collage by Halliwell at its auction on September 22.
It is described as “an important part of 1960s cultural history as well as an engaging piece of art work” and has an estimate of £3000-5000.
However experts predict it could reach well above £10,000.
The couple, who infamously defaced Islington public library books and were jailed for the crime, lived in the north London borough after meeting at RADA (Royal Academy of Dramatic Art) in 1951.
Now the museum wants to bring the art work back to the borough nearly 50 years after their deaths.
Islington Heritage Service has launched the public appeal.
Mark Aston, local history manager at Islington Local History Centre and Museum hopes to raise up to £5000 from public donations which could help him apply to the Arts Fund to subsidise the rest.
Aston said he was alerted to the sale by an article on ATG. He said: “We have wanted to build up our collection. This screen is very rare and I couldn’t miss the opportunity.”
Aston bought a 1966 collage by Halliwell three years ago for £2800 for the museum at an auction at Stacey’s in Essex which was televised on BBC’s Flog It!
The museum unveiled it in February 2014 and it is now in a permanent display of book jackets that were artistically defaced by Halliwell and Orton.
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