The 23-year-old dad to Peaches' two children overcame his grief to perform the song as a crowd of mourners said their goodbyes to Peaches, who died at the young age of 25.
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"Tom was incredibly brave to sing because he was obviously tremendously upset," a source told The Sun.
Jools Holland, a friend of Peaches' dad Sir Bob Geldof, accompanied the lead singer of S.C.U.M. on the piano at the service held on Easter Monday in Davington, near Faversham in Kent.
A source said: "It felt like I was at a music gig, it was so lovely, a real celebration of her life. Tom was incredibly brave to sing because he was obviously tremendously upset and struggling to contain his emotions."
Peaches' father bravely led the tributes to the 25-year-old mum-of-two at St Mary Magdalene and St Lawrence church, where just 18 months previously he had given her away at her wedding to Thomas Cohen. Peaches' mother Paula Yates was also laid to rest there in 2000.
His heartbreaking eulogy has been described as "the bravest thing" by his close friend, Alan McGee.
Queen drummer Roger Taylor also sang at the private service, while Peaches' sister Tiger Lily, 17, read the W.B. Yeats poem That The Night Come.
Pixie Geldof, 23, gave a personal eulogy, while eldest sister Fifi, 31, read the Henry Scott-Holland prayer Death is Nothing At All.
Peaches passed away on 7 April at her home in Wroxham, Kent. The cause of her death is still unknown.
She leaves behind two young sons Astala, 23 months, and Phaedra, 11 months, with her husband Thomas.
Peaches' ashes were said to have been scattered at her father's neighbouring Davington Priory country estate, where she grew up.