It'll be wet, but not snowing or that cold. Tho when I say, "not that cold", I really mean, that it'll mostly be above freezing. Reasonable chance of it freezing overnight (not guaranteed, but likely. January/February is when it gets really cold. November is mostly wet.

All that being said? It's UK (Scotland, for me) - the only guarantee is that there's no guarantee... *g*

Ooh, apparently google is my friend:
November 2005 (http://www.bbc.co.uk/weather/ukweather/year_review/reviews/nov2005_review.shtml)
November 2004 (http://www.bbc.co.uk/weather/ukweather/year_review/reviews/nov2004_review.shtml).

Scotland/North of England is usually colder than the south of England.

I have no idea how feasible this is, nor how safe for an Australian travelling alone

I... have no idea. I have no fear of flying down to London myself, nor being in Glasgow/going over to Edinburgh myself. I've never felt threatened in the UK, but I'm native and I haven't done a lot of travelling in the UK. (And I'm also largely oblivious people.)

Also, I find trains expensive in the UK. I have no idea what we're like in relation to elsewhere in the world, but I find it expensive.