Surely all my telephone/broadband wiring belongs to BT and they need to fix my fault or complete alterations?

No this is a common misconception. The only part of your telephone line that BT (or other service provider) are responsible for is the cable up to your master point (known as Network Terminating Equipment or NTE). Past this point any wiring within your premises is your property. If a BT/Openreach engineer attends site and proves any fault within your property (including damage or damp issues up to the master) then a charge of up to £130 will be applied to your bill, plus a large hourly rate to resolve the issue.
Contact me before speaking to your service provider, as it could save you a LOT of money!