Originally intended for an administrative role in the navy, Allen apparently held a purser’s warrant before being commissioned lieutenant on 17 May 1756. He was promoted commander of the fireship Pluto 16 on 21 November 1761, and he retained her through to December of the following year.
He was posted captain to the Juno 32 on 20 June 1765, which he retained until paid off in June 1766. From the summer of 1767 he commanded the Glasgow 20, serving on the North American station and returning home to unemployment when she was paid off in May 1771.
In the summer of 1778 Allen joined the Chatham 50, which had recently returned from North America, and in which he sailed from Portsmouth on 27 March 1779 with a convoy for Gibraltar in the company of the Thetis 32, Captain John Gell. The Chatham returned with the Lisbon convoy in November, during which voyage her consort, the Hussar 28, Captain Elliot Salter, captured the Spanish Nuestra Señora del Buen Confeso 64, carrying but twenty-six guns. Allen himself was less fortunate in respect of prize-money, as the funds from a capture he made at the end of the summer were lost when his agents failed. The Chatham was paid off at the end of the year and taken into dock for repairs, following which Allen recommissioned her and continued to command her in the Channel and North Sea until October 1780, capturing the cutter Alexandrine 10 on 18 May.
His next command was that of the newly-commissioned Sceptre 64, which he held from January 1781 in the Channel fleet. In late 1781 he replaced the invalided Captain Sir Digby Dent aboard the Cumberland 74, sailing in February 1782 with Commodore Sir Richard Bickerton’s reinforcements for the East Indies station. The Cumberland fought in the last of Vice-Admiral Sir Edward Hughes actions with the French at the Battle of Cuddalore on 20 June 1783, losing two men killed and eleven wounded. Allen brought her home to England to pay her off in June 1784 and did not see any further service.
He became a rear-admiral on 1 February 1793, a vice admiral on 4 July 1794 and an admiral on 14 February 1799. He died on 24 October 1804 at Lambeth.
He married Catherine Douglas at Salisbury, Wiltshire, on 24 January 1776, and one of their sons, William Edward Hughes Allen, entered the Navy in 1800 and rose to the rank of commander. Additionally the couple had another son and two daughters.