As others have said, CH is a closed system so the mains water pressure shouldn’t matter.
I would check that the CH has pressure, should have a pressure gauge on the boiler, and it should be between 1 and 2 bar.
I would then check the boiler fires up, when you switch the heating on.
I would then check the pump is running (put a screwdriver on the pump, and test if you can feel the vibration against your ear)
I would then check any motorized values and manually check they are open, and open them if they aren’t and see if that helps
You could also, attempt to bleed a single radiator, and see if it gets hot as you are bleeding it as that would also imply a pump problem.
Essentially, though if you have pressure, the boiler is firing, the pumps running, the valves are open and you still don’t have heat, and the bleeding trick doesn’t work, at this point I would ring a plumber…..