Henry “Harry” Eastham came from a footballing family in Blackpool. His father had played professionally for the town’s club, while his elder brother, George, became an England international. Harry was therefore the uncle of the younger George Eastham, who later played for Newcastle United, Arsenal and Stoke City and was a member of England’s 1966 World Cup-winning squad. Harry’s own route into professional football began with Blackpool Central Juniors before he joined Blackpool’s staff in July 1934, aged seventeen. He played for their “A” team but had yet to make a Football League appearance when Liverpool signed him in February 1936. A contemporary Portsmouth Evening News profile put the fee at £1,000 and noted the resemblance between Harry and his brother George, both inside-rights admired for their ability to turn and control the ball.
Eastham made his Liverpool debut in a 2–1 victory over Arsenal at Anfield on 31 October 1936. His first goal followed three weeks later in a memorable 5–2 win at Manchester United, where he joined Alf Hanson and hat-trick scorer Fred Howe on the scoresheet. He finished his first season with twenty-one league appearances and two goals, establishing himself as a serious contender for a place in Liverpool’s attack. He began 1937/38 as the regular inside-right, playing in Liverpool’s opening twelve League matches, but subsequently lost his place to Phil Taylor and made only three further League appearances that season. His opportunities became more limited in 1938/39, when he played seven League games. The outbreak of war then interrupted his career just as he entered what should have been his prime years. During the wartime competitions he appeared for Liverpool and guested for several other clubs, including Blackpool, Bolton Wanderers, Brighton & Hove Albion, Leeds United and Newcastle United.
When the First Division resumed in 1946, Eastham was twenty-nine. He returned to make nineteen league appearances in Liverpool’s championship-winning season, enough to qualify for a winner’s medal. Although he did not score during the campaign, his appearances accounted for almost half of Liverpool’s League programme and made him an important member of the squad that secured the club’s fifth championship. He also played twice in the FA Cup that season. That success proved to be the end of his first-team career at Anfield. Eastham did not appear for the senior side in 1947/48 and moved to Tranmere Rovers in May 1948, having made sixty-eight recognised competitive appearances and scored four goals for Liverpool. At Prenton Park he enjoyed a more sustained run of first-team football, making 154 league appearances over five seasons in the Third Division North. He subsequently joined Accrington Stanley before continuing in non-League football with Netherfield and Rolls Royce.