Consider the 20th century British composers(those born after, say, 1860) who
were given a knighthood:
(O.M.=Order of Merit; C.H.=Companion of Honour. An O.M. is a very great honour indeed; there are only 24 members of the Order at any one time and it therefore, effectively, outranks a knighthood).
Sir Edward German
Sir Arthur Somervell
Sir Granville Bantock
Sir Henry Walford Davies(Master of the King's Music)
Sir John Blackwood McEwen (as Principal of the Royal Academy of Music)
Sir Hamilton Harty(also conductor)
Sir Arnold Bax (Master of the King's Music)
Sir George Dyson
Sir Arthur Bliss, C.H. (Master of the Queen's Music)
Sir Eugene Goossens (also conductor)
Sir William Walton, O.M.
Sir Lennox Berkeley
Sir Michael Tippett, O.M., C.H.
Dame Elizabeth Maconchy
Sir Andrzej Panufnik
Sir Malcolm Arnold
Sir Peter Maxwell Davies (Master of the Queen's Music)
Sir Harrison Birtwistle
Sir Richard Rodney Bennett
Sir John Tavener
Benjamin Britten was made a Life Peer as Lord Britten in 1976, a few months before he died. He had refused a knighthood but had accepted an O.M. and a C.H..
Ralph Vaughan Williams refused a knighthood but had an O.M.
Frederick Delius and Herbert Howells both had the C.H.
Composers with the lesser order of C.B.E.(Companion of the British Empire):
William Alwyn
John Linton Gardner
Alun Hoddinott
Gordon Jacob
Elisabeth Lutyens
James MacMillan
William Mathias
John McCabe
Robin Orr
Alan Rawsthorne
Edmund Rubbra
Thomas Wilson
and at the bottom of the pile-
Daniel Jones, O.B.E.
George Lloyd, O.B.E.
Arthur Butterworth, M.B.E.
You will note those British composers whose names do not appear in these lists

A word of caution though. We do know that Vaughan Williams and Britten refused knighthoods and that Robert Simpson refused a C.B.E. I suspect that Holst refused honours offered.
Whether the composers who are listed deserved the particular honours awarded I leave to others to judge-although it has always slightly puzzled me that Lennox Berkeley got a knighthood ahead of Alwyn, Rawsthorne and Rubbra.
Oh....and I profoundly apologise to those composers who received honours which I have failed to pick up on
