Cook and Beckingham, pictured, were unveiled as the joint successors to Tim Dixon in September, former Bromley Green boss Cook returning to Reachfields following a previous spell as assistant manager and Beckingham arriving after standing down as manager of East Grinstead Town.
In a statement announcing Beckingham's departure, officials said several candidates were being considered to take over as their new first team coach after Darren Anslow also left the club. Assistant manager Mark Lane will continue in his role and will be alongside Cook on Tuesday night when he takes sole charge for the first time at Whitstable Town.
Hythe Town chairman Paul Markland said: “Clive and Tony came to us as a managerial pairing based on their longstanding friendship so it’s a shame that things haven’t worked out, however it’s probably better for all concerned to realise this early on.
Hythe Town
"We now have a more conventional manager/assistant manager set up. We thank Tony for his support and wish him and Darren all the best for the future."
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