In general I have never noticed a preference for which side to walk on on a pathway, in the UK or anywhere else. People tend to stick with the peleton.
2
If there is no pavement, keep to the right-hand side of the road so that you can see oncoming traffic.
(http://www.highwaycodeuk.co.uk/rules-for-pedestrians---gener...)
For the Americans, pavement in British English means sidewalk :)
After learning this (in school road safety lessons I think?) in general I always assumed you should walk on the right as a pedestrian for consistency (even though the highway code doesn't contain any rules for sidewalks) but it's not universally observed, particularly in London where there are so many foreign tourists.
Also confusingly, when Swedes are about to make a left turn they keep to the far right instead of the more logical left, and vice versa.
With the four-way you describe, I would usually expect to see a single light, with it blinking yellow on the primary route, and blinky red on the secondary road.
That said, people do tend to walk on the right-hand side as far as I can tell, following the traffic. So, no consistency. The 'no pavement' is already exceptional. Walking on the other side of the road in that case is just part of that experience.. :)
You walk facing traffic not for consistency, but so that you can see what's trying to hit you. It doesn't apply so much for pavement/sidewalk, but you'll certainly live longer when there's no clearly separated area for peds.
Signs in corridors in stations can say either "keep left" or "keep right" depending on what's more convenient for corridor layout. Escalators are always stand right, walk left.
(Out of interest and because the article also mentions it, there is no concept of jaywalking in England and I've read that it is not in any way illegal for pedestrians to cross against a red light. However drivers rarely defer to pedestrians even at marked crossings.)
(Out of further interest, in Paris the suburban trains use left-hand running like the national network, but the metro runs on the right.)
As with any invention, attribution to any one person or even nation is difficult; the UK did have the first machine-powered rail trains and the first intercity machine-powered passenger rail service (Liverpool and Manchester Railway).
The metro looks to be British as well, though: the Metropolitan Railway, now part of London Underground, opened in 1863, and John Fowler was its chief engineer. The first electric-powered underground railway was the City and South London Railway, opened in 1890, James Henry Greathead as its chief engineer. (Budapest metro opening in 1896, Paris metro opening in 1900.)