The first advert is from the 'Kid Again' campaign, organised by Transport for London and the London Safety Camera Partnership; this implies that if you can't (or don't) drive then you're not really an adult. The second advert is from Change4Life, an NHS campaign (I copied the photo from this blog); this campaign is encouraging people to do more exercise, e.g. by walking or cycling rather than driving. The TfL website also has information about cycling, with the slogan "You're better off by bike".
Personally, I can drive, and I think it's a useful skill. However, I know several people who can't drive, and it doesn't seem to restrict their freedom. This is particularly the case in London, since we have a pretty good public transport system. The only time I drive nowadays is for SJA or if I'm going outside London (e.g. I'll be driving to Wales and back next weekend).
I used to own a car (and later a motorbike); the trap is that once you have that option available, it becomes the default, even for short journeys. For instance, when I lived in the Docklands, some friends lived nearby: it was about a 20 minute walk, but if I went round to see them it was easy to hop in the car instead. Nowadays I cycle quite a lot, which would be handy for a journey like that: it would be quicker than walking, but I'd still get some exercise and be a bit more eco-friendly. When I do my weekly shopping, I catch the bus to the supermarket: that way I can carry several bags back with me, and it only costs me £2 (on Oyster) for the round trip.
I think the main problem nowadays is that it's normal to own a car, so people don't consider alternatives. However, this must be a relatively recent phenomenon, given that cars haven't existed for that long. I did some digging on the web, and came across a page about car ownership. Quoting from that: "There were only 8,000 cars in the whole of Britain at the start of the 20th century. By the end of the century the car population had soared to 21 million." I'm not sure whether it's feasible to reverse this trend, but I think it's worthwhile to at least mention the possibility.