Babi - I have to say that many British people do absolutely no walking! This county, East Lothian (formerly Haddingtonshire) probably has a higher number of walkers than elsewhere because it has beautiful countryside, the hills aren't too steep, and it has a huge number of young retired people who are very 'outdoorsy' - in fact, almost the whole population could be described as that. I think if you looked at any of our major cities you would find that most people there are couch potatoes.
You're also absolutely right in saying that our countryside is more 'manageable' than yours - we can go for short-ish walks and see quite a lot, especially down here in the Central Belt. In Aberdeenshire, where I used to live, there are longer distances between places - though walking is still popular - and on the north west coast the mountains are, by our low standards, huge; you can't just potter up them in your trainers, they are for serious hill walkers (like my son) and proper climbers.
There are a lot of walking clubs in the UK - the Ramblers Association is the best known and very well supported.
I like walking because you can do it at your own pace, it isn't competitive, and you get to see the countryside whilst you're doing it. Although I do also swim, I don't like most other sports, and I really loathe the gym - I just can't see any pleasure in running on a machine in a hot sweaty room. I also like walking in cities - I have walked around most of Edinburgh, large parts of London, bits of Birmingham and Manchester, and so on - you see so much more that way. My parents-in-law live in the Lake District, so we have done quite a bit of walking there, but it is always so busy compared to Scotland, you sometimes feel like you're in the Piccadilly Circus of hill walking - and the towns, like Ambleside and Windermere, are constantly over-run with visitors. Parents-in-law chose to live outside the national park partly for cost reasons but also to get away from the seething hoards.
Today I was driving back from Haddington in glorious sunshine, the sea in the Firth was blue, everything felt so springlike, and I knew exactly why so many people like living here and so few move away - we have all the joys of the countryside but are only 25 minutes from central Edinburgh - how good is that?
I hope you have good weather where you are,
Rosemary