Intermittent hot water problem?

I have a worcester boiler (can't remember model name) which seems to have an intermittent problem where shower runs from hot to cold. It fires up and then suddenly cuts out and the cold water is the result. No engineers have worked out what the problem is. I have asked BG to come out and quote for a new boiler and they have pointed out the overflow is not going to an external wall (going to waste pipe)...they didn't say whether this might be the cause or not. Please could someone confirm if this is a possibility or any other reasons/ fixes to remedy the problem.