Thomson was born in 1969 in Salford, Lancashire to Mary McAleer, who gave him up for adoption six weeks later. He was adopted from the Catholic Children’s Rescue Society by Andrew and Marita Thomson, a businessman and a bookseller from Didsbury. He has one younger brother, Ben (born to his adoptive parents). He attended All Hallows Catholic High School near Preston, leaving with three O-levels. He then attended Runshaw College between 1985 and 1987, studying for four A-levels, including theatre studies. He was described as "clearly [having] a talent for comedy".
Following this, he turned down a scholarship in America to study drama at Manchester Polytechnic.