He was born in London, the son of William Hamilton, a Scottish bencher of Lincoln's Inn, and succeeded his father in 1754.

His maiden speech, delivered on 13 November 1755, during the debate on the address, which excited Horace Walpole's admiration, is generally supposed to have been his only effort in the House of Commons.

But the nickname "Single Speech" is undoubtedly misleading, and Hamilton is known to have spoken with success on other occasions, both in the House of Commons and in the Irish parliament.

Hamilton was thought very highly of by Samuel Johnson, and it is certain that he was strongly opposed to the British taxation of America.

Two of his speeches in the Irish House of Commons, and some other miscellaneous works—including previously unpublished notes on the Corn Laws by Johnson—were published by Edmond Malone after his death under the title Parliamentary Logick.