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This sounds like you have an un balanced shower valve. Meaning the cold is fed from the main and the hot from a header tank. You dont state what led up to the problem occurring or if it has happened all the time.
Im Norfolk UK your fine. Ok so a combi boiler.
Heres some questions
Is this the only bath tap are all the other taps basin or kitchen sink or shower?
if the answer is yes
This is your plate heat exchanger, its unable to keep the FLOW of water hot . So when you turn on a cold tap it obviously decreases the flow and your plate heat exchanger can keep up.
The other taps and showers in your property use small bore pipe work, so although the pressure is good they don't use the flow that a bath tap does.
Hope this makes sense to you.
Your cold water goes into a boiler and then into a plate heat exchanger, heat from the central heating water passes along copper plates which transfer the heat through the plate to the cold water, heating it up to serve your taps.
when the plates get scaled or dirty they dont transfer the heat as good.
So when your 22mm Bath taps are flat out your are passing more water through that exchanger than it can heat up.
When you turn on a cold tap in your house you obviously reduce the flow of water through the heat exchanger and it can then keep up.
To prove this for yourself turn on the hot bath tap full allow it to get warm and then turn it half off, you should find the water gets hotter.
I'm not explaning to you very well so I will opt out and see if anyone else can help you better.
Basically the more flow of hot water the less heat due to dirt in the plate heat exchanger.
Hope you get your problem resolved soon.
Best regards brian