Sounds like the fuel pump relays knackered Ross, sometimes they prime but dont run when cranking or in your case, dont prime but run whilst cranking.

open it up and closely inspect all the solder joints! usualy crack.

to bridge the relay to make the pump run constantly with ignition (NOT RECOMMENDED for anything other than testing !!) get a piece of fairly thick piece of fused wire and bridge pins 87 & 30.

HTH.