A handwritten poem by Keats, I stood tiptoe upon a little hill (estimate £40,000-45,000), is another highlight in the two-part sale in Bond Street, the first on April 10, the second on May 8.
Works by Sylvia Plath, W.H. Auden and Charlotte Brontë will also be on offer.
Poetry: Poetical Manuscripts and Portraits of Poets follows the Papers & Portraits sale at Bonhams on March 29, 2011, in which Mr Davids consigned works by his close friend Ted Hughes, Sir Isaac Newton, Keats and James Joyce among others.
The former head of Sotheby's printed books department, who has been a dealer and collector for more than 40 years, specialised in manuscripts and portraits of writers, artists and musicians, collecting material from a number of eminent figures from British history, including Winston Churchill, Siegfried Sassoon and the poet William Blake.
Betjeman wrote the draft of The Arrest of Oscar Wilde at the Cadogan Hotel in 1932 or early 1933 on the headed notepaper of The Architectural Review where he was assistant editor from 1930-35. It was published in the June 1933 edition of the Oxford and Cambridge magazine.
This is the only draft of the poem ever known to be offered at auction and carries a guide price of £5000-6000.
"It would now be impossible for the present collection to be even approximately replicated," said Mr Davids.