He was at school in Amersham, Buckinghamshire, under Dr Croke and was admitted at Christ's College, Cambridge, on 21 March 1639.
He was awarded MA in 1640 and admitted at the Middle Temple in the same year.
In August 1660, Montagu was elected MP for Dover in the Convention Parliament.
In 1661 he was re-elected MP for Dover in the Cavalier Parliament and sat until 1679.
Montagu died in 1681 and was buried at St Katharine-by-the-Tower in July.