That is fine, try and buy a programmable room thermostat, then you only need a pair of existing cables.
You will need a battery powered thermostat to make this happen
Looking at the instructions (follow the link above) it will be fine and fit in the existing space with the existing wiring
If there is a neutral at the site of the current thermostat then it will just need isolating safely
you mention a " neutral" in your text, are you assuming it is currently wired to a "3 wire" , I not sure..
Yes, a lot of the older ones had a live, neutral and switch wire
You only need to use the live and the switch wire
When these two are connected your heating fires
If its a 3 or 2 wire system There is an existing cable system between the existing "Room stat "and the boiler
so a 2 core...... I connect to the current Marked terminals, at each end ....and on a 3 wire system keep the live and the "switched live" return lead ...and isolate the Neutral if it has one.