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.