The first thing is to find out, is if the existing room thermostat has been disconnected or is still wired up and is faulty. If so, you might just need a new thermostat, or fresh batteries if it is of the type that uses them.
With just one room thermostat in the property, it will control all of the radiators based on the temperature of the room in which the thermostat is located. So, when that room reaches the set temperature, the whole heating system goes off. For that reason it should be located a room that is among the last to heat up, and then the TRV's control the temperature in the rest of the rooms to stop them overheating. So even with a room thermostat, you would still be using the TRV's for control of the other rooms.
The thermostat also needs to be located in the right position and that's not as easy as it sounds. Consider:
It should be in a room that is not effected by other sources of heat such as an open fire, cooking equipment, or direct sunlight etc. It should not be somewhere draughty, or too close to a window, especially if it's one that is opened in the winter.
Secondly it should be in a cool room, preferably one of the last to warm up. That way the other rooms will be warm enough, (but not overheated because of their TRV’s) before the room thermostat switches the entire heating system off.
The radiator(s) in the room with the room thermostat installed should not have a TRV fitted. Otherwise the TRV could interfere with the operation of the room thermostat.
The thermostat should be mounted about 1.5 metres from the floor, and not close to, or above a radiator.
Preferably it should not be on an outside wall, (although if you have well insulated walls, this is not quite so crucial.)
It should be in an area where air can circulate easily, not in a corner, or hidden behind curtains or furniture.
There are TRV's on all the rads.......Its a bit of a nuisance constantly turning radiator valves up and down in each room.
The whole idea of TRV's is that you shouldn't have to adjust them. I haven't adjusted any of mine for years. The function of TRV's is that they are set to the temperature that you find comfortable for each room and then they maintain it with out any adjustment. For example: 21 degrees in reception rooms, 18 degrees in the bedrooms, 22 in the bathrooms etc. If you find that you are having to adjust them to maintain a comfortable temperature, either you are not using them properly, or they are faulty.
the boiler is old style, as in it heats the water to store in a tank.
Nothing wrong with that. Such systems are still installed today. However, if your hot water system is what's known as a 'gravity system' where the cylinder doesn't have thermostatic control and relies on natural circulation of water through it to heat the contents, then whilst a room thermostat will control the room temperature, it won't be able to provide a 'boiler interlock' that switches off the boiler completely when under its control without modification. Having said that, Standard TRV's don't have this facility anyway, so even now, when heat is not required, the boiler will keep running just to keep itself hot and wasting fuel.