One thing to be aware is that UK houses have much smaller rooms, and from Oz you will notice a distinct lack of bathrooms / toilets.
Think kitchen, enclosed with doors, living room enclosed with doors, the only bathroom and bedrooms upstairs. That might not sound much of a problem but when you have muddy kids running up the stairs to use the toilet you might.
There is unlikly to be a wash room unless you are getting a new property, and no electrical sockets i the bathroom - just one for a shaver (it iis two pin, the rest of the house is three pin, but different three pin to yours).
Your visa should allow you NHS treatment and school places, I know student visas do, so resident ones should.
You don't have to put your kids in school, if you do then the schools are quite strict about time taken outside school holidays if you want to holiday in term time. Consider home schooling if you fancy skipping around Europe with the kids. In reality you don't need to do much education wise if you do spend time travelling.
Distances are shorter but there is more traffic so a journey can take longer than expected.
Air travel is not as cheap as it was but you can easily visit European cities as city breaks.
You will want to spend some time in London, you can do day trips but if you stay for a weekend it can be cheaper to book a break with tickets to a show (Lion king / Shrek are child friendly).
One piece of advice for your first winter. When your car frosts over (it will happen overnight, and can happen in a few hours while you are in a shopping centre) pour COLD water over it, or use defrosting spray. Warm/hot water will crack the windscreen.
Also if it snows, set off in second gear.
Be prepared for your kids to spend a lot longer inside because of the weather. Swimming pools are mostly inside.
If you get satellite TV you can watch ausie rules football, but I don't think you can on cable and not on terrestreal.
Alternatively Walkabout - Aus themed pub chain - show games on Monday afternoons.