Okay,
First things first.......
Your BT Master socket is in a boiler room that has no power....
Are you entirely sure that is the only master socket in your home ? it seems highly unusual for that to be the location as BT would not normally expect you to sit in a boiler room to answer your phone - after all if you had a cordless phone you would require power to run the cordless base station. I would question that being the master socket from the start unless your one hundred percent sure. Do not take the call centre in india's word that it will be the socket with the BT logo on it as you can have multiples of those. If you have a BT line from a telegraph pole, follow the cable to your house and observe where it breaks into the walls - thats where your master socket will be.
If you are encountering problems with an extension being run off of the master socket then you need to establish what is going on with that. If its a cheap extension kit e.g. something from argos then yes it can encounter noise - a good way to check is plug a normal phone into the extension and listen for static on the line. A good extension will give a minor degredation of dsl performance but nothing drastic.
Finally, your wifi connection.... your dsl router does not have to be connected to the bt line for you to test your wifi connection. try putting everying in the same room and see what happens - I would suspect if you had driver problems you would get no connection rather than a bad connection.
If you could provide more info on what you have done to establish connection spead/reliability we can try some more things to eliminate the problems. Of benefit would be to find out if your router is 802.11 A/B/G or N and if possible what your wireless adapter is compatible with - We can then narrow it down from there.