Thank you for the suggestions!
I had already put decoupling caps on the display, and put a large(ish) cap on the supply in general to try and filter it. However, I'll look at the power supply issue shortly, presently it's a 9 volt 600mA wall wart. The whole project is just a lash up on a breadboard to get some nominal values for later use.
I also think that it's causing interference to digital radio signals, but to be fair the reception can be poor so it's difficult to tell!
David.