Sounds like the divert valve.
It works by having the ‘hot’ circuit and the ‘cold’ circuit on opposite sides of a rubber diaphragm. When you open a hot tap (or the shower) the ‘hot’ pressure drops, and the diaphragm moves. It is attached to a shaft, which pokes out of the end of the valve body, and in turn pushes a microswitch which will fire up the boiler thus turning the ‘hot’ water hot.
The diaphragm eventually breaks down, and stops moving. It can shift on the initial demand, then the pressure equalises and it moves back – and the boiler thinks you don’t need any more hot water, and shuts off.
I have had to replace 2 of these on my 4-year old Worcester Bosch 28CDi.
It is a DIY-able job, and doesn’t involve touching the Gas side. However, I wouldn’t recommend it if you are not in possession of reasonable DIY skills.
The valve is pretty buried in the 28CDI – the rest look similar. Lots of things to take out before you get to the valve. Lots of potential leaks when reassembling.
Replacement valves are about £180 IIRC, but last time I did one, I got a replacement diaphragm for £15. 1st time took me about 3 hours.
There is a decent repair manual available online here –
http://www.newtonnet.co.uk/house/boiler/servicemanual.pdf
You can do a ‘quick fix’ if you glue a lump of something onto the end of the actuator shaft, but it will only buy you about a week at best.
HTH.