I think if you are coming from Norway, the NHS is not a plus point. Neither is "all the people". Going into central London drives me absolutely nuts.
If you have children, you need to know that nurseries are extortionate. Like £50-75 per DAY per child. Children are not let out to play unless the play equipment have been wiped off and dry if it has been raining, if it is raining, no outdoors play.
Education can be hit and miss, unless you are prepared to pay (3-4k per term), or live in a very expensive area to be in catchment of a good school, or be able prove your allegiance to some sort of religion. But good education is good, probably better than in Norway.
Honestly, after living here again for three years after spending three years in Norway, I dont think life in general is that much cheaper here (London). I have also developed asthma since I came back, and what is more shocking to me is not all the murders and teen murders which seem to happen weekly, but that London is one of the most polluted cities in Europe.
I moved to London from Norway when I was 20. Loved it, but went back for three years, and I certainly dont love it as much now as I did between the ages 20 and 37!