Reserve warships can use wet berths

Would keeping a reserve fleet require enough dry docks for all its ships?

No. Ships can remain in suitable wet basins, and Britain retains infrastructure from its larger fleet.

Reserve ships do not need to occupy dry docks continuously. A suitable wet basin can hold them, and Britain retains basins and bases built for a larger navy. Some of that infrastructure is unused. The accumulation of retired nuclear submarines is given as an example of existing berthing space, alongside the separate problem of completing their disposal.