Laxton was born in Oundle, Northamptonshire, England, the son of John Laxton, a local merchant. Laxton was educated at the grammar school in Oundle, which was to slip into decline and ultimately close over the next half century. Upon leaving school Laxton travelled to London to become an apprentice to the grocers in London. Upon finishing his seven year apprenticeship in 1519 he gained his freedom and prospered. Having gained his livery Laxton was elected to the Court of Assistants, and was made Junior warden on 16 July 1534. In May 1536 he was elected Upper Master of the Grocer's Company and, after serving as Sheriff of London for 1541, became Lord Mayor of London in 1544. He later acquired a knighthood.
Sir William Laxton died on the night of 27 July 1556, and is buried at St Mary Aldermary church in London. Under the terms of his will Sir William left property in London to the Grocer's Company on condition that they paid annual sums of money for the support and maintenance of a new school in Oundle to replace the old grammar school which he had attended. Oundle School is now one of the leading independent schools in the United Kingdom.
He married a widow, Joan daughter of William Kirkeby. His stepson Sir Thomas Lodge would also become Lord Mayor of London in 1562.