Griffiths, who played Radcliffe's uncle Vernon Dursley in the wizard franchise, was laid to rest at the Holy Trinity church in Stratford-upon-Avon, West Midlands of England, where poet William Shakespeare was buried, reported Daily Mirror.
"Daniel was clearly very fond of Richard, as anyone who ever met him was, and was crying quite openly in church. "It was a beautiful service and Richard would have been touched by how many people turned up to say goodbye.
Richard was a tremendous character and the service was full of laughter and tears as his life was remembered with immense warmth and affection," a source said.
Many stars attended the service and laid flowers including Judi Dench, who appeared with him in 'Pirates of the Caribbean: On Stranger Tides' and Griffiths' 'Withnail and I' co-star Richard E Grant, whose message read, "To my beloved Uncle Monty, chin chin, all my love Richard E Grant." Actor Nigel Havers, comedian Jack Whitehall, who was Griffiths' godson and 'Downton Abbey' creator Julian Fellowes also attended the funeral.
A photo of Griffiths' as his famous role of Hector from 'The History Boys' was printed for each of the guests, accompanied by the poem 'Late Fragment' by Raymond Carver.
A selection of verses were read out, with former Bond girl Carmen Du Sautoy reading from 'Ecclesiastes' and TV star Penelope Wilton reciting Griffiths' favourite poem by Edward Lear, 'The Owl and the Pussycat'. Griffiths' passed away in March after complications following heart surgery. The actor is survived by his wife of 33 years Heather Gibson.