Mark was born in Horne, Surrey to farmer and amateur entertainer Bernard Kempner, and former land-girl Mary Kempner. He went to Michael Hall school, and excelled in particular, in the many drama classes. Mark worked on the family farm until meeting wife Anna at 18. They married in 1982. They have two children, both of whom are also professional actors. Soon after leaving school, Mark worked on a Kibbutz in Israel for a year and in that time, started up a touring comedy drama group. The group toured other Kibbutz's performing comedy sketches.