The song by Long John Baldry that became a number one hit in Britain in 1967 is "Let the Heartaches Begin." This song reached the top of the UK charts and was his most significant hit, spending two weeks at number one starting from November 22nd, 1967. It was also his only UK top 10 single that year. For more information, you can refer to the Wikipedia page on the List of UK top-ten singles in 1967.