Six months later, 21 April 1689, he was appointed captain of HMS Centurion, which ship was lost in Plymouth Sound in a violent storm on 25 December of the same year.

In November 1698 he was appointed to HMS Resolution, and during the next year was senior officer at Spithead, with a special commission for commanding in chief and holding courts-martial (23 February 1699).

His application did not meet with immediate success; in June he was turned over to the Tilbury, and continued to command the squadron in the Downs, at the Nore, and in the North Sea, till, on 1 March 1702–3, he was promoted to rear-admiral, and directed to hoist his flag on board HMS Mary, then fitting out at Woolwich.

As Lady Beaumont's second son, George, who, on the death of his elder brother, had succeeded to the title and estates, was unmarried and appointed a lord commissioner of the admiralty in 1714, the implied statement that the family was dependent on Basil is curious.

Beaumont's portrait, by Michael Dahl, is in the Painted Hall at Greenwich, to which it was presented by King George IV; it is that of a comely young man.