I would suggest a full install with a NEW master installed. Leave the phone wiring there are you may be able to use some for extensions and even if you are star wired, there is a way to convert to daisy chain (no-perfect but doable). Stone walls may well give problems with DECT phone and WiFi.
TO get full coverage, you may well have to run in Cat5e and several WAPs.
Chose a decent ISP - TT have already ruled themselves out by demonstrating their lack of knowledge or desire to assist.
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