 William was the third, but eldest surviving son of Sir Clifford Clifton and Frances Finch, daughter of Sir Heneage Finch former Speaker of the House of Commons.He was christened in St Mary Abbots, Kensington on 7 April 1663.His paternal grandfather was Sir Gervase Clifton, 1st Baronet and paternal grandmother was Lady Frances Clifford, daughter of Francis Clifford, 4th Earl of Cumberland

He succeeded his father in ownership of the Clifton estates in 1670, and succeeded his cousin Sir Gervase Clifton, 2nd Baronet, to the baronetcy in 1676.