Middle-aged: Because walking is cheap and uses up a whole day for very little money. So it's ideal for parents with kids, who are (surprise) mostly middle-aged. Why no younger walkers on these tours? Well, younger walkers are usually out doing their own thing, and usually over harder routes. Walking tours are mainly aimed at casual walkers, so you get families with kids, or retired people, or people who used to walk but haven't for a while. Middle-aged again.
Middle-class: Now that's a little more surprising. But it's quite easy to explain if you look at transport. In Ewan McColl's day, there was plenty of cheap transport into the hills. These days it's all gone - one or two buses a day is standard for most places, so if you live more than a couple of miles from the hills and you've not got a car then you basically can't go walking. But that's what you get when you sell off public services like buses and trains, and run them for profit instead of as a service for public benefit.
White: You don't have to do too much walking to see that this is true. The main root cause though has to be that immigrants have often come from areas where walking is a matter of necessity - walking for enjoyment isn't a cultural feature, and indeed could be dangerous. (Or if they've come from America which is the other way round - pedestrians are seen as "second-class citizens" and so walking for enjoyment likewise isn't a cultural feature.) I think most walkers have started off by their parents walking, and that just isn't an element for most non-Europeans. Other walkers start through Scouts, D of E or some other group, and I guess that's where people of non-European origin would start, but ramping up numbers takes generations. Also there's the fact that colour and income are somewhat linked, so the comments on "middle-class" are equally valid.