I believe that no. is a 15mm compression so this would be your man
https://www.screwfix.com/p/flomasta-compression-stop-ends-15mm-2-pack/65021
It could be that someone has removed the nut & olive & screwed the 1/2" thread directly into a female fitting in which case you can put ptfe around the...
Then plan A is certainly possible.
If you have a combi boiler many manufacturers insist on a mini ev being fitted.
It is often a failing ball valve that causes noise problems or a dripping 1/4 turn tap.
You could try pump up ev to 1 bar then turn mains back on & see what pressure the ev is...
The lower fascia panel will pull off. Usually pull upwards to detach it from the lift off clips.
This will give you much better access.
You may have room for a second ball valve in the cistern but I have no idea how you think that would help.
I would first of all
Turn off water and open tap to release pressure.
Attach compressor/foot pump/bike pump to shock arrestor and pump up to 3.5 bar.
Turn water back on and see if problem has gone away.
Check that your stop tap is open all the way and back 1/2 turn
Clean the seating before fitting the new ones and a smear of silicone grease never hurts.
If they are not a common size, tapmagician has an 18 sheets of A4 list of dimensions to choose from.
You could always fit one of these, blended supply to wc and set it to about 20 degrees. Would draw mostly from the hot pipe till temperature achieved and then continue to fill cistern with mostly cold.
https://www.screwfix.com/p/flomasta-thermostatic-mixing-valve-15mm/684fa
This will be full of...
Start with the easy exposed one. Run shower till body is hot, usually on left hand side.
Run a not so hot tap. Cold water flowing through the shower will rapidly cool the LHS of this shower.
If it is not this one then you will have to repeat by pulling the faceplate forward on the concealed...
It will be a temperature controlled mixer so shower mixer not basin mixer.
While running a not so hot tap you may hear something if you put your ear to temperature control knob.
If they are exposed valves the temperature check by feel will be easy but if they are concealed and you can access the...
Could be a faulty check valve on a shower.
If you run one of your not so hot taps and then wander around and feel your shower valves is one of them particularly cold?