Usually the red wire is the 'live' and would be in terminal 1 (TL=Thermostat Live) and the yellow wire the 'switched live' that controls the heating and would be in terminal 2. (H=Heat) So, from your photos, yours wires are transposed. Wired like this, the thermostat will work, but not be as accurate as it should be.
Having said that, it's possible, but probably unlikely, that they are also transposed at the other end of the cable. If so, this is one of the rare instances where two wrongs make a right.
[Apart from the wire colours not conforming to the usual convention]. Someone who is competent with a multimeter would be able to test and confirm this quickly.
If you go for a battery operated thermostat that requires only two wires, these would be the two wires you would need, and with a non mechanical thermostat it doesn't matter which way around they are connected.
If not required, the neutral in terminal 3 is insulated / isolated and positioned safely out of the way.
When it comes to choosing a new thermostat there are two main types:
Programmable Room Thermostat: This allows you to set different temperatures at different times of the day and becomes the sole controlling device for the central heating. Any existing timeswitch / programmer controlling the heating becomes redundant and should be decommissioned, or set to be permanently 'on' 24/7. Programmable room thermostats are available as 'smart thermostats' which often have fancy features and can be controlled remotely via an app.
Room Thermostat: a replacement for what you have now, and the existing timeswitch / programmer controls the on / off times
If you select a thermostat you like the features / look of, post back details and someone will be able to give you specific help to make the swap. If you do, I suggest that you post your question in the Plumbing & Central Heating forum, where the folks in the know about these things hang out.
This forum is called 'Your Projects' and its use defined as:
