Kay practised as a doctor for six years, and his 2017 memoir of the profession This Is Going To Hurt became a bestseller and was filmed with Ben Whishaw in a BBC series for which the writer won a Bafta.
He said of himself and his siblings: "We're all in medicine and law, which is a huge success for Jewish parents, getting proper professions out of us."
Kay, who lives in Oxfordshire with his husband James and their two young children, said that "religion dilutes through the generations". "These days, we do Hanukkah candles plus a Christmas tree, so there's a bit of background for the kids. I don't think religion had a huge part in my childhood. It has even less in my children's."
In an interview in the JC in 2017, Kay recalled how he gone to cheder as a child and had a bar mitzvah, and that he went to synagogue no more than once a year.
Kay also told the i about how there are still occasions when he is reminded of his old profession.
"I've been in a few 'Is there a doctor in the house?' situations. Increasingly I have to weigh up - am I any more use being 15 years out of the game, than a plumber?
"There have been medical emergencies during my live shows, due to the law of averages when playing to a total of 350,000 people. You hear a kerfuffle, the lights go up and someone will say, 'is there a doctor in the house?' Usually, there are so many doctors, the safest place to be in the UK at any time is at one of my shows."
He was speaking as his new show for children, Dexter Procter is being shown on CBBC, about a 10-year-old doctor and starring Peter Serafinowicz and Jameela Jamil.