Potterton Puma 100/100e - hot water but no heating!?

Hope someone can shed some light on this problem before we have to get a new boiler installed.

Our hot water is working just fine but we have no heating. It started off as a gradual thing with no heating on the ground floor (we live in a town house), all the radiators have now ceased to work. With the exception of the two bathroom radiators...but I believe they may be on because they could be plumbed into the hot water pipes?

A plumber has been round and has checked for blocked or collapsed valves which are fine. He has changed the pump incase it was that and has emptied the boiler/radiators and refilled them along with bleeding all radiators.

He now thinks it could be the heat exchange..does that sound right?

The boiler gets up to temperature and then trips out.

Would be grateful if someone could shed some light on this for us as we are freezing and have a 4 month old baby.

Thanks

Sarah