The musician, who died at his New York home on Christmas Eve aged 76 after a short illness, produced more than 200 works for the concert hall but is perhaps best known for his film and television scores.
His credits include Four Weddings and a Funeral, Far from the Madding Crowd and Murder on the Orient Express – his film work gained him Oscar nominations while he was knighted for Services to Music in 1998.
Sir Richard was also a well-respected writer and performer of jazz songs and known for work experimenting with European avant-garde techniques.
Chris Butler, Chief Operating Officer and Head of Publishing for the Music Sales Group, said: ‘Richard was the most complete musician of his generation – lavishly gifted as a composer, performer and entertainer in a multiplicity of styles and genres.
‘He was a loyal friend to music, musicians, and music publishing and we will remember him with great respect and affection.’
Sir Richard had been living in New York for more than 20 years prior to his death.