If you are just looking for a simple replacement thermostat, then a wired thermostat made by any the major manufacturers [Honeywell, Danfoss, Drayton, Siemens] would be fine. Avoid cheap thermostats available from ''online shopping" sites, some are not really suited for use with UK heating systems, and the quality can be poor. With thermostats as most things you get what you pay for.
You don't have to replace both thermostats, from an electrical point of view, they are all simply on/off switches.
If one section of the heating associated with a thermostat has failed, this is not the most common failure point, so be sure it is the thermostat before you replace it.
Wireless thermostats tend to be more expensive than wired versions, and as in your case the wires are already in place they offer you no advantage, and may be a bit more involved to install. A wired thermostat on the other hand will be a straight swap for the existing one.
You do not need a programmable thermostat (one that controls both time and temperature) you could fit one, but if you did, the existing time controls need to be set to be permanently on 24/7
Some thermostats require 3 wire connections, the 2 switching wires and a neutral, others only have the 2 switching wires. This may effect your choice of replacement.
If you opened up the existing Honeywell, and it has been correctly installed, I would expect to see the following:
Live supply to terminal 1
Neutral to terminal 2
Switched live to terminal 3
On the other hand if it has been incorrectly installed there may only be wires connected to terminals 1 & 3. It will still work, but not be as accurate as it should be.
Therefore if there are only two wires, then you would need a battery powered thermostat, that only needs a two wire connection.
If you are looking for a smart thermostat, there is only one that I know of that is suitable for a 2 wire installation and that's Nest-e, but unless you want to rewire, the thermostat receiver would be located where the existing thermostat is presently sited.
Other smart thermostats (the most popular on this site are Nest Gen-3, Hive & Tado) will require a minimum of 3 wires, and once again the positioning of the receiver should be considered. If there is a stored hot water system (hot water cylinder) that also would be controlled by the smart thermostat, the wiring becomes more complicated.
