Your new budget looks pretty good to me, although I hadn't realised that day care would be so expensive!
A small tip regarding TV/phone/broadband... some companies, e.g. Virgin Media and Sky are currently offering deals where you can get a basic cable TV package, unlimited broadband internet and a phone line rental all for about £30 per month (for a certain amount of time - usually 12 months). This doesn't include your phone calls, but would work out a lot cheaper than your budget estimate of £105 per month for the three services individually.
Also, I know you're budgeting for future car trips around the UK and abroad, but if you're in London, chances are you'll be using the tube to travel around the city more than a car when you get one. I currently drive 200 miles a week and my gas costs are £80 per month, so unless you'll be driving the equivalent of about 30 miles every day, you probably won't have to allocate so much to gasoline - did a quick distance search for Sweden and judging by the fuel efficiency of my car, a trip to Sweden and back should cost somewhere in the region of £300 or so for gas, so if Sweden was the only place you were driving to, then that's only 3 months worth of your budget.
Since you haven't moved here yet, it's difficult to tell how much you'll actually end up spending in each category, so you may find that you've under-budgeted for some things and over-budgeted for others, but overall, it seems fairly reasonable to me.
