What's funny is that it's only that way because of all the people driving rather than cycling. If the people who could get to where they're going without a car (bike/bus/train/whatever) used those alternative forms of transportation, then it would make the roads much clearer for the few people who actually need to drive (trades/emergency vehicles, etc.).
Both the total throughput and average speed of these roads would increase if more people were on bikes and buses. Unfortunately if it were to ever happen I fear people would just see the clearer roads and think, "Hey, the roads are clear now, I should drive again!" and we'd be right back to square one.
This was filmed in London, which actually has some of the best cycling infrastructure in the UK (though that's a low bar to pass). It seems, however, that he's taking a route that happens to not have much of that infrastructure on it.
Though as you say, people should be able to cycle however they please, and it is enshrined in UK law that cyclists are not required to use cycling infrastructure. In this case I'd say he's going fast enough that he'd be a danger to the slower cyclists and pedestrians on the cycle paths and multi-use pathways, so riding on the road makes more sense anyway.