So what you're saying is that the immersion heats the water, but the boiler doesn't.
Difficult to diagnose from here because it all depends on how the system is set up. It may well be that there is a cylinder stat on the immersion. Not the one in the element, but a separate one that tells the boiler when to heat up the water.
HW usually has preference over the CH. In your case, it's not responding. Have a look around the cylinder for a stat of some kind. It may simply need turning up or replacing. I'm going by experience of conventional cylinders here. If you have an unvented cylinder (HW comes out at full mains pressure), then it may be more complicated and would certainly need someone to look at it to investigate.