As relatives of Thomas become increasingly concerned for his wellbeing, Peaches' father Sir Bob Geldof was the one who spoke during the service.
Peaches Geldof and Thomas Cohen in 2013
A source said: "Bob was stoic and held it together a number of times. His voice only broke a couple of times."
Speaking of 23-year-old Thomas, the source said: "Thomas, however, is struggling to cope and was walking around in a daze... His family are very worried about him."
The source went on to say to The Sun newspaper: "Bob wanted all the celebrities and her friends to be there for her children. He has made it clear he doesn’t want the kids to be emotionally struggling on their own, and for Tom to have as much help as he needs."
"He also made it clear that this wasn’t about one day. Peaches would want them there for her children in the future," the source added.
Kate Moss, Nick Grimshaw and Jools Holland all showed up to the ceremony on Monday to show their respects to their late friend, and Kate was seen crying on the shoulder of her husband Jamie Hince.
Afterwards, many of the 150 friends and family attended a wake at Sir Bob’s house near to the church, although it was "more like an after-party".
"There were lots of stories and anecdotes about Peaches," said the source.
Peaches was found dead in her home in Kent two weeks ago. The young mother’s service was held in the same church where she married Thomas two years ago in a fairy-tale wedding, and where Peaches’ mother Paula Yates was also laid to rest in 2000.
Her funeral service included a hand-painted coffin with portraits of her whole family, including two-year-old Astala and her youngest son, Phaedra, who turns one this week.
Recent reports have suggested that Thomas will sell the family home as he has told friends that he cannot return to their family home where his wife was found.
Peaches’ ashes are expected to be scattered today at the property of her father.