Cartwright was a native of Long Island, Bahamas.[2] He was elected to the Bahamas House of Assembly, the lower house of Parliament, in 1949 as a representative of Cat Island.[1] He served in parliament for seven years.[1] Outside politics, Cartwright worked as a realtor before becoming a magazine publisher.[2]
In 1953, William Cartwright, who owned The Bahamas Review purchased The Nassau Herald, on the death of it co-founder, Jack Stanley Lowe.[3] Cyril Stevenson, who worked as a journalist at The Nassau Guardian became editor of the Herald.[4] Later that year, Cartwright and Stevenson travelled to London to cover the coronation for The Bahamas Review.[5] While there, they met with representatives of the Labour Party.[5] They also travelled to Jamaica where they met with members of the Jamaican Labour Party and the People's National Party.[5]
When they returned to Nassau, Cartwright and Stevenson joined with Henry Milton Taylor to found the Progressive Liberal Party (PLP), the first national political party in the Bahamas.[1][2] Taylor became chair, Cartwright became the treasurer, and Stevenson became the secretary-general of the new party.[3]