Cattini, who lived in Hertfordshire, co-founded the Tornados in 1961. Their instrumental 'Telstar' spent five weeks at the top of the UK chart in 1962, and they became the first British group to top the US Billboard Hot 100.
As a session musician, he played on number one hits including Tom Jones' 'Green, Green Grass of Home', Dusty Springfield's 'You Don't Have To Say You Love Me' and Tony Christie's '(Is This the Way to) Amarillo?'. He also played on Engelbert Humperdinck's 'Release Me', Love Affair's 'Everlasting Love' and Johnny Kidd & The Pirates' 'Shakin' All Over'.
In a Facebook post, Christie described Cattini as 'a world class musician but also a world class gentleman'. He wrote: 'So very sad to hear that the great Clem Cattini, drummer of the Tornados and prolific session drummer has passed away. Clem played on more number 1 records than any other British drummer. Proud to have known him. My condolences and love to his family.'
Carl Palmer, drummer with Emerson, Lake & Palmer and Asia, said: 'The drummers all over the UK owe you a lot for opening the door for all of us.'
North London band the Equals, who topped the charts in 1968 with 'Baby Come Back', posted on social media: 'The legendary Clem Cattini, a true powerhouse of percussion and one of the most prolific drummers in British recording history. An absolute legend who leaves behind an incredible musical legacy.'
His other credits included recording with Paul Weller, the Kinks and the Wombles. He played drums on all 11 tracks of 'Thrillington', an instrumental reworking of Paul and Linda McCartney's album 'Ram', released under the pseudonym Percy 'Thrills' Thrillington. Cattini toured with Cliff Richard and Roy Orbison, and performed on television with the Top of the Pops orchestra. He was played by James Corden in the 2008 film 'Telstar', about Tornados producer Joe Meek.
Cattini was born to Italian parents in Stoke Newington, north London, in August 1937.