Swap a wired doorbell for a wireless one, safely disconnecting the old wiring and fixing the new push button to any wall.
Altering fixed wiring (for example removing a hardwired fused connection unit) falls under Part P of the Building Regulations. Capping off and leaving wiring safely isolated is fine for most people; removing accessories from the fixed wiring is notifiable work in England if you're not a registered electrician.
Before you start: Which electrical jobs can I do myself? Part P explained
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