Okay I'll note that down. However I'm a bit confused- if they need me to show that we've lived together for me to get the FLR, how can I apply for it now? I've just arrived and plan to marry within a month or so, so my name won't be on anything until then. Will I have to wait a few months before applying for FLR then? Which means I can't start work for at least a few months?
No, you don't have to wait - if you don't have anything with your name on it, then you just explain that you've only just started living together and don't have anything yet.
However, you should just start getting your name on things ASAP anyway, because it will make things easier in the long run - you don't have to wait until you're married to do it.
You'll need proof of your UK address in order to register with a GP and open a bank account anyway, so I would get your name on bills, lease, council tax etc. as soon as you can (i.e. now), even if you aren't married yet. You can always update your married name on the accounts after the wedding.