Annesley was born in Dublin, Ireland to Francis Annesley, 1st Viscount Valentia, and his first wife Dorothy, daughter of Sir John Philipps, Bt, of Picton Castle. He was educated at Magdalen College, Oxford, from which he graduated in 1634 as a Bachelor of Arts; that year, he was admitted into Lincoln's Inn. Having made the grand tour he returned to Ireland; and being employed by Parliament on a mission to the Duke of Ormonde, now reduced to the last extremities, he succeeded in concluding a treaty with him on 19 June 1647, thus securing the country from complete subjection to the rebels. In April 1647 he was returned for Radnorshire to the House of Commons.