Thanks Polyglot. I just had a look at high current gain opto-isolators and it looks like one will do nicely.
I did a bit more reading yesterday and figured out that I would lose the ability to drive the existing neon directly whatever I did. That being the case I'll give the opto-isolator a go. (I can always drive an led (or even the existing neon) from the output signal easily enough.) I'll try the HCPL-3760 ('cos it has 240v ac input and internal bridge rectifier) and it'd be useful to get to know it anyway. If that doesn't work I'll try a higher current gain one. Thanks for putting me on to that.