Morris joined Third Division South club Brentford in 1921. With the Bees having finished second-from-bottom in their first season in the league, he helped inspire the side to a 9th-place finish in the 1921–22 season, top-scoring with 17 goals in 39 appearances. He top-scored again in the 1922–23 season, but departed Griffin Park in February 1923. Morris made 63 appearances and scored 30 goals during his 18 months with the Bees.
Millwall
Morris signed for Third Division South club Millwall in February 1923 for a £750 fee. Over the course of his time with the club, he scored 30 goals in 76 appearances for the Lions as the club consistently challenged for promotion to the Second Division. He departed The Den in May 1925.
Swansea Town
Morris moved back up to the Second Division to sign for Swansea Town in May 1925. He remained with the club for one season, making just 9 appearances.
Swindon Town
Morris dropped back down to the Third Division South to sign for Swindon Town in June 1926 for a £110 fee. He had a brilliant start to his career at the County Ground, netting hat-tricks in each of his first two matches. He scored in the following two matches to set a club record of scoring in each of his first four games, which stood until it was matched in September 2014 by Jonathan Obika. Flourishing under Sam Allen's management, Morris finished the 1926–27 season with 48 goals from 43 league games, but problems with the defence meant the Robins could only manage a fifth-place finish. He also became the first Swindon player to score five goals in a single game, which came in a win over Queens Park Rangers. He repeated the feat in a 5–1 demolition of Norwich City in April 1930. He also went on a run of scoring in 11 consecutive games during the season, scoring 19 goals. Despite failing to win any silverware, Morris was top scorer in each of his seven seasons with Swindon and scored 18 hat-tricks. In addition, he was top scorer in the Third Division South in the 1926–27 and 1927–28 seasons and his record for the 1926–27 season stands at the eighth-highest single-season goal tally in Football League history. Deemed too old by incoming manager Ted Vizard, Morris was released prior to the start of the 1933–34 season. During his seven years with Swindon, Morris scored 229 goals in 279 games and as of 2018 is still the club's leading goalscorer. His overall league goalscoring record is the 17th-highest in English football history. In 1955, 22 years after leaving the County Ground, Morris applied for a coaching role with the club, but was rejected. In a poll to celebrate the Football League's 125th anniversary, Morris was voted Swindon's greatest-ever player by the club's supporters.
Clapton Orient
Morris signed for Third Division South club Clapton Orient in July 1933 and scored eight goals in 13 appearances during the 1933–34 season.
Morris was Jewish. Though he was observant of the faith, he played on Saturdays during his football career and would only refuse to play on high holidays. He was educated at the Jews' Free School in London and was a member of the Brady Street Boys' Club. He served in the Middlesex Regiment during the First World War. Morris was married to Edith and had a son, Jack and a daughter, Estelle, who died from polio in 1937 at the age of eight. Morris, Edith and Jack emigrated shortly afterwards to Gothenburg, Sweden, where Morris worked at the British Consulate. The outbreak of the Second World War in 1939 and the invasion of Norway by the Germans the following year saw Morris and his family remain in neutral Sweden until the end of the war. Through his job at the consulate, Morris helped escaped POWs return to the UK. The family emigrated to the United States after the war, with Harry and Edith working for the British Information Services in New York City. They retired to San Mateo, California, where Edith died in 1984, followed a year later by Harry.
Honours
Football League Third Division South Golden Boot : 1926–27, 1927–28
