The system needs to be clean and wired properly
if the pump is not wired back to hhe boiler it probably doesn't have a pump overrun which can cause issues with The heat exchanger.
Have you had anyone out to look at it yet
No, no-one has had a look yet, was just asking on here first to see what you all thought, but I'll definitely get someone over asap. If I got someone round to do a service would that pick up the problems or does the service just look at a set list of things and they don't really investigate anything else, if you know what I mean?
In terms of the wiring, there is a timer up by the hot water cylinder that you set the heating/water times for the boiler to come on, is that what you are on about?