In my own house I used a hard wired, when the battery went flat it stopped working, mother house had a Honeywell Y6630D which is wireless but not programmable, it was a really good thermostat, OK not best suited for a condensating boiler, as it used a mark/space system to stop over shooting, but it had a fail safe built in, not signal and after 30 minutes it switched off, i.e failed safe, however once the programmer turned off, then no central heating.
So I thought better to use a programmable thermostat, so instead of switching off, it turned the temperature down, so I got a Horstmann HRFS-1 wireless thermostat which reading the spec seemed to be the bees knees, it was actually cheaper than the Honeywell T6630D and I thought I was a very good son selecting this thermostat.
That was until I came to visit and found the room at 35°C, for what every reason it had lost the link, and it seemed it did not retry, turn it to 40°C and back to 20°C and it worked again, it did this a few times, and I returned to the Honeywell Y6630D as it was far more reliable.
I then fitted Energenie MiHome TRV heads which were programmable and ensured even if the wall thermostat did stick on, the set temperature would not be exceeded.
I will not claim they were to start with A1, the TRV was on the return, and there was a problem that the radiator got really hot before the heat reached the TRV, and I had to adjust the lock shield valve to stop the over shoot, however once set they worked well, and as my mothers health deteriorated we moved into and got a second pair.
As said the Honeywell Y6630D was not the best for a modulating condensing boiler as it used a mark/space system to stop over shoot, but it worked well, even if it did result in using over the amount of gas it should have done.
They were claimed to work with Nest, so on my mothers death we took the TRV heads to out new house and bought Nest Gen 3 to work with them, however it seems Nest withdrew support, so using the Smart Phone app they did change temperature with Nest, but using the dial, schedule, or geofencing they failed to follow. So had to be set simply to same schedule as Nest Gen 3.
So the bluetooth eQ-3 TRV heads bought for upstairs rooms worked just as well as the energenie but at ¼ of the cost, may be not a good comparison since now using an oil fired boiler, so not modulating, however my advice is based on my errors.
Point is working A1 as far as control is concerned and working in an economic way is not the same, so either expensive wireless thermostat or any old cheap wired programmable thermostat. So to go wireless your likely looking at 6 times the price of doing the same thing hard wired.
And all the wall thermostat does is turn off the boiler when warm weather arrives, it does not control the room temperature the TRV does that.
Learn form my error.