Many of the stars behind The Young Ones, the comedy hit that established his reputation, were among mourners who attended the service at St George's Church in picturesque Dittisham, Devon.
Edmondson, a university friend of Mayall who went on to play the show's punk Vyvyan, acted as a pall-bearer, while Nigel Planer (who played hippy Neil) and Alexei Sayle (landlord Jerzei Balowski) were among more than 100 people who paid their respects.
Elton, who co-wrote the show, was also there to celebrate the life of the comic actor with whom he formed a strong bond as a student in Manchester.
Mayall - also known for his roles in TV hits such as Bottom, The New Statesman and Blackadder - died last week aged 56 at his home in Barnes, south-west London. He also had a home in Devon.
Friends from throughout his career attended the service, and filled the church with cheers and clapping as they recalled his achievements and his humour.
Mourners also included friends from his appearances in Channel 4 series Comic Strip Presents, director and actor Peter Richardson, Dawn French and Edmondson's wife Jennifer Saunders.
Others who filed into the church to an organ performance of Procol Harum's A Whiter Shade Of Pale included Alan Rickman and Ruby Wax.
Prior to the service, Mayall's widow Barbara asked fans for their "thoughts and prayers" during the private ceremony, which was led by Father Will Hazlewood.