To be honest, if the boys are hiking nature loving, and you are not into city life, choosing London over Norway is bloody insane! 
Even if you like suburban living. Because thats all you gonna get.
Hiking in England is a bit of a joke. It is something we do because it is something easy to do as a family together. But even the boys have realized it is nothing compared to walking along deserted beaches for hours, or hiking up to 1200 meters from sea level and down again, or long paths through forests, and spending days crossing tundra between peaks walking from cabin to cabin in the wild. Taking out your fishing rod and catching river salmon or trout.
Your boys sound a lot like mine. (Skateboarding is an urban activity they have taken up in England) They like hiking, mountain trekking, fresh or salt water fishing , spending time on the beach jumping from rock to rock trying not to get their feet wet (this you can also do in England
) tenting in the wild, cycling in the mountains, foraging for blueberries in the automn. And lets not forget skiing. Cross country and downhill.
In England, it pales into a dusty mud filled treks along farmers fields, through "forests" or woodland which is no less than a triangle between main roads that it takes 30 minutes to walk through, with rubbish, and road dust. And even that is busy...
Hiking in the uk, unless you go to the Lake District or Scotland, is like this:
You drive a couple of hours, park your car. (Less if you are in Surrey as opposed to south west London) You have downloaded to your Ipad, or printed out your hiking guide (try register with walkingworld.com). You spend 10 minutes along the road, an hour crossing a field, then another 10 minutes along a road, then 20 minutes crossing some woodland, another 10 minutes along a road, 40 minutes crossing a field, some woodland, and if you are lucky you are back to your car, as otherwise you have an hours walk along the road, or you catch a bus back to your car. When I say road, I dont mean paths, but proper tarmacked roads where cars and coaches and lorries whizz past at break neck speed!
Your life sounds pretty good where it is!
Coming to London to go hiking in the English country side? I think you have been watching too many Jane Austin adaptions. England is extremely industrial and built up. Even the Peak District, The Lake District and Wales with Mount Snowdon are tiny areas, which are mostly farmland as opposed to nature, when you compare it to the big American National parks and wilderness, or Norwegian wilderness. Think about it, Great Britain is very small geographically, with 67 million people! Norway is slightly bigger, and with 5 million people.....
My cousins husband had a bit of a mid life crisis when he hit 40. He decided to walk across Norway through the mountains, not following any roads, but sometimes head down to villages and shops for supplies. (Not that often in fairness, as he brought his rifle for hunting small game, and his fishing rod for fish) It took him 6 months, then he could not be bothered and he came home and asked for a divorce. They had 5 kids. This summer, they remarried, after 10 years apart. My aunt wore the same dress to their second wedding as to their first. But I digress.
You just need to have an open mind and prepare yourself that it will be 2 years of something very different. Britain is tiny. It takes my husband just two days to cycle from the east to the west. Now we are back here, we live for the holidays back to Norway, where we can spend time in real nature.