It's just about flow sensing. When you draw hot water this creates pressure against a rubber membrane (diaphragm) it doesn't matter whether this is positive or negative,m the facty is the diaphragm moves, which makes an electrical contact, which tells the pump to come on, fan to come on and burner to ignite, then you get hot water (if the hydraulic part of the diverter valve is working correctly).
Now it is usually the diaphragm gone manky with age and not having sufficient flexibility or worse torn, that doesn't move the microswitch with sufficient force to commence the necessary chain of events. The part is about £7 at daylight robery stockists and £1.99 at others.
Labour to diagnose and fit £45 for businesses out of lucrative areas, could be anything from £75 to £150 in lucrative markets.
If you live in a lucrative market consider moving to a far better place. Unless you are there because you are rich or stupid or both.
Of course this is not a diagnosis, one needs to be sat in front of boiler to do that correctly, part of what you pay for, the other part is a safety inspection advise and as required appropriate action.