Racing on the public highway is an offence. I don't know how it relates to cycles, but I wouldn't be surprised if the whole 'vehicle/not a motorised vehicle' thing didn't add some confusion to it all. So I expect as such a big thing is made of it that different permissions are needed to hold an actual race than to hold an event that doesn't involve racing. I have a vague recollection that there's also a requirement for a race to be sanctioned by the national body at some level while an event doesn't need to be. It definitely used to be for cars that you could hold a point to point event (basically a tarmac rally) without needing permission providing you weren't timing the competitors for speed. So they would set a course and remind everyone that they had to keep to a 30mph average (or whatever) and then add in problems, normally finding out your route, that had to be solved during your driving time (meaning that suddenly a 30mph average was a much tougher ask) this was legal because they weren't, by the letter of the law, racing.