I plan to relocate the base station from the lounge (where there's no neutral feed in the wiring to the old conventional thermostat, just a live that the old thermostat switched on) to the utility room where I can easily "feed" the base station with live and neutral so that it works properly and then the base can switch on the boiler.

Remember that the wireless thermostat allows you to not just relocate the temperature sensing portion of the thermostat but you can also move the base station to very near the boiler.