Montagu was the only son of Sir James Montagu, MP and judge, and his first wife Tufton Wray, daughter of Sir William Wray, 1st Baronet, of Ashby, Lincolnshire.
At the 1734 general election, Richard Eliot brought him in as MP for St Germans.
He did not vote on the Spanish convention in 1739 or the place bill in 1740, and withdrew on a motion to remove Walpole in February 1741.
At the 1754 general election he was returned unopposed as MP for Northampton on the interest of his cousin, George Montagu-Dunk, 2nd Earl of Halifax.
His widow became well known in society and was an intimate friend of Mary, dowager-countess of Gower (the widow of John Leveson-Gower, 1st Earl Gower), and of Mary Delany, in whose published 'Correspondence' she frequently figures as 'my Mrs Montague', in order to distinguish her from the better known Elizabeth Montagu.