A given propeller could appear on either or on both sources. The PTL/1 list does not normally include all propeller types that have ever been fitted previously to a particular aircraft type, but only those which are known to be popular and likely to be universally suitable. Use of any other type of propeller other than those shown on the PTL/1 or on an existing Permit to Fly Operating Limitations document would necessitate embarking on the LAA Engineering modification procedure, making an application and paying a fee in the normal way. In the case of in-flight adjustable propellers, due to the several variables in setting them up and the effect their installation often has on the aircraft's weight and balance, a propeller change application form is required, followed by flight testing authorised by LAA Engineering, to verify the safe operation of the aircraft and compliance with the appropriate requirements.
If you are relying on this list, rather than the Operating Limitations to demonstrate that the propeller fitted to your aircraft is approved then it is important that you keep the PTL/1 document safe along with the Permit to Fly and be able to provide it to your LAA inspector on request, especially at the occasion of a Permit renewal inspection.