Other than bits of the Scottish Highlands and Islands we don't really get extreme weather in the UK. Even winter temps rarely drop more than a degree or so below freezing, so cold by Aussie standards but nothing to cause traffic problems. Even though the UK is famous for rain we rarely get the torrential downpours you might be used to in tropical parts, we tend to get a little bit all the time rather than one rainy season (I just looked up the rainfall figures and apparently Brisbane gets nearly twice as much rain as London.) Once every ten years or so we get a few inches of snow that cause traffic chaos for a few days, the level of fuss this causes gives an indication of how unusual this sort of thing is. I would not expect there to be any weather related travel problems.
The sun does set early in winter but it's not necessarily a problem depending on what type of activities you want to do, which leads on to your next question: what things are open?
A lot of predominately outdoors or rural things do shut down over winter. This includes a lot of things like gardens and some of the more rural Country Houses and a lot of National Trust properties. Also some seaside towns tend to shut some attractions down out of season. This again probably won't be a problem for you as the sort of places that shut down aren't where you'll want to be on a chilly, wet, winters day. As long as you're not planning a hiking holiday you'll be fine. Towns and cities are unaffected by winter closings, in fact museums and theatres etc. will probably have more business as we tend to make the most of the outdoorsy things in summer.
I'm not clear if you are planning to use a motor home this trip? If you are be aware that many camp sites close over winter.