His last known club was Ashford Town.
For the 1979-80 season Ashford Town were placed in the Southern Division.
Beveney moving to Ashford Town once fully fit.
He later played non-league football for Ashford Town and Sittingbourne.
He then had spells as manager with Ashford Town and Hastings United.
Ashford Town was his next club before becoming player coach at Northfleet.
He made two appearances for Margate before being appointed player-manager of Ashford Town.
A week later his scored his first goal for the club in their 2-2 draw with Ashford Town.
The 1997-98 campaign saw the club finish as runners-up in the league, losing out to Ashford Town.
He left to join Ashford Town in 1937.