He made his debut for the "Saints" in a Second Division game away to West Bromwich Albion on 5 October 1946 on the left wing, where he soon became settled, scoring a brace in a 5–1 victory over Plymouth Argyle on 26 October. Manager Bill Dodgin preferred him on the right, however,, teaming up with the ageing Bill Rochford. This role was not to Grant's liking and his form slumped. Although he was transfer-listed in August 1948, he remained with Southampton for the next two seasons, used occasionally as replacement for Eric Day. In 1948–49 he seemed settled back on the left before he lost his place to Bill Heaton. After a rather frustrating time, he joined Cardiff City in March 1950 with Ernie Stevenson coming to the south coast in exchange. In his four seasons at The Dell he made 64 appearances scoring 13 goals.
Cardiff City
Soon after his move to Ninian Park, manager Cyril Spiers moved him to centre forward following the arrival of Mike Tiddy, where his devastating turn of speed immediately produced instant rewards, with 14 goals coming in the 1950–51 season as Cardiff finished in third place in the Second Division. The following season Cardiff went one better finishing in second place, thus gaining promotion to the First Division. During Cardiff's promotion season Grant was top scorer with 26 goals, the first 19 of which were at home. Shortly after Cardiff secured their place in the top flight, Grant's superb form earned him a call up to the England 'B' team for a match against their French equivalents on 22 May 1952. Unfortunately for Grant the match ended in a resounding 7–1 victory for the French which brought his international career to an end. He spent two further seasons with Cardiff in the First Division where, jointly with Ken Chisholm, he was again top scorer in 1953–54 with 12 goals as Cardiff reached tenth place in the league table. After four and a half seasons at Cardiff City, Grant was sold to Ipswich Town in October 1954 for a fee of £7,500. In his career at Cardiff, Grant made a total of 159 league and FA Cup appearances scoring 67 goals.
Ipswich Town
At Ipswich he was manager Scott Duncan's most expensive signing at £7,500. At the end of Grant's first season at Portman Road, Ipswich were relegated to the Third Division South. In August 1955 Duncan resigned and was replaced as manager by Grant's former Southampton teammate, Alf Ramsey. In 1955–56 Grant contributed 16 goals as Town finished in third place, missing promotion by one point. Injuries and loss of form restricted Grant to 12 appearances in 1956–57. After three years with Ipswich, Grant dropped out of the Football League to join Llanelli as player-manager.