 Wrench was born in 1882, in Brookeborough, County Fermanagh, part of the Province of Ulster in Ireland, the son of the Rt.Hon.Frederick Stringer Wrench (1849–1926), an Irish Land Commissioner, Deputy Lieutenant and Privy Councillor, by his wife Charlotte Mary Bellingham (1848–1935), sister of Sir Henry Bellingham, 4th Baronet.