I was thinking "UK" rather than world wide, and not on
closed roads.
Cyclists are allowed to race without road closures, no-one else is though. The authorities are very strict when it comes to motorcycles or motor vehicles doing so. I'm involved with classic trials events, where cars and bikes travel around 200 miles between off-road hill sections. Vehicles are only allowed an average road speed of 30 mph on a fixed route and anyone arriving too early at a section (which can be worked out quite easily) is deemed to have been speeding and may well be excluded. If a competitor gets a speeding ticket 24 hours before or after a trial, or becomes involved in a road accident they are obliged to declare it and are thus disqualified.
However, it has been mentioned quite recently that a proposed change in policy may allow applications for public roads to be closed for motorsports events here, too.