Multiple entries

I'm a UK passport holder so I know that I can visit Georgia without a visa, but can I enter, then go to Azerbaijan, then back to Georgia (ie can I make multiple entries?)
Thanks

Yes. "Without a visa" means "without a visa," full stop. It doesn't matter if you want to enter twice or twenty times.

Correct.
A few years ago I went from Georgia to Armenia, back to Georgia and then on to Azerbaijan. No problems.

Don't forget to obtain a visa for Azerbaijan.