When can I mow?

You can cut it any time but in early spring, don't cut it too short. Raise the blades if you want to cut it now and go back to normal length when it starts growing strongly in spring

Yep, I totally agree with Andrew, I scarified and cut my lawn today and even laid a little bit of turf. I lifted the blades a few notches above the normal seasonal cut, it certainly made it look better after my new dog has been churning it up, mind you he manages to send the moss flying into the air which is good.
In March I will scarify it again as I have loads of moss and I will aerate it by stabbing a fork in and giving the ground a very gently lift (every 12") to get air underneath, I'll scatter some soil over the bare patches and sow some grass seed, in really bad patches I'll replace with turf, it is really cheap at B&Q at the moment and reasonable quality.
I got a huge compliment today on my turf laying
My husband said he would water it when I had finished, I said you have to make sure the joins are well watered. When he came to water later he said he couldn't see the joins - that is a turf laying compliment!!
It may be better to hire an aerater from a tool hire shop if you have a large amount of lawn, I might consider doing that. That job is a pain, but well worth it in the long run for a better quality lawn.
Probably more information than you needed but best of luck A x