Xantia 2.0 HDi starting problem?

I have a '99 Xantia 2.0 HDi. For some months I have heard the clicking (constant) of a relay at the O/S/R of the car. At least I was told it was a relay. "Not to worry". Now having problems starting: engine turns over OK, but nothing; then, sometimes hours later, it will start. Then it won't! (Relay has stopped clicking.) AA started it the other day by whacking the underside of the tank. Garage thinks I need a replacement LP Pump. Hm. Sometimes, on 'ignition', we hear the pump priming in the tank - and then it fires OK, and will continue to run for as long as you like. So - if it will do that, surely the pump is OK (?). I'm suspecting the relay but, because the problem is so sporadic.....? I'm reluctant to shell out £££'s for a new pump if it's not necessary. Can someone say whether, if the engine (once started) will continue to run indefinitely, the pump should be OK?