Alf Jennings arrived at Underhill, aged just 17, in time for the 1920/21 season and scored his first Barnet goal in a 4-2 defeat at home to Civil Service. On 11/9/20, he made his competitive debut for Barnet in an Athenian League game away at Bromley, Barnet losing 1-0. The Barnet team was; Green, H King, Woolner , Skeggs, Allen, T King, Pett, Watkins, Jennings, Mason, Thompson.
A week later, Jennings scored a hat trick in a 5-1 demolition of Kingstonian at Underhill in the league and a few weeks later went one better, scoring four as Barnet hammered Luton Vauxhall 8-0 in the FA Cup First qualifying round.
Jennings, ably abbeted by Ernie Watkins and J Fillistone, became a regular scorer for Barnet, scoring another four goals in a 5-0 home win over Wood Green Town, two in the 5-1 defeat of Woolwich Polytechnic in the London Senior Cup and hat tricks away at Cheshunt, in the Herts Charity Cup semi-final and at home to St Albans in the Athenian League. His form was such that a number of professional clubs were chasing his signature.
However, Alf’s career at Underhill was a short one as in January 1921, it was announced that he would be going with his parents to New Zealand for a while but in the end his family emigrated to Australia. His last game for Barnet was a goalless draw at Chelmsford in the Athenian League. Jennings finished top scorer for the season with 31 goals despite not playing in the last few months. Jennings also represented Hertfordshire in County matches and scored 4 goals in 1920 playing for Herts.
In Australia, Jennings played for a club called Granville who were runners up in the New South Wales League Championship while Jennings was in the team and he also captained the New South Wales state team. He later returned to England and played for Tottenham Hotspur.