Hey, I'm allowed the weekend off, aren't I?
My immediate thought is that they can do this. Private roads don't have to be gated and they are just that - a track that allows a person access to their land (or someone else access over the land, with permission - called an easement).
There are different categories of right of way, footpath, bridleway, byway, restricted byway are the main ones - plus carriageway (a conventional public road allowing access to all types of traffic). However the width of the right of way is established over many years. A footpath is usually the width of a human - say one metre wide but it doesn't have to be. A bridleway is often the width of a horse - say two metres - but again it doesn't have to be. I live on a public bridleway which is about four metres wide - just as well because it acts as our access for our vehicles (how landowners can establish a right of do that is another story - I won't bore you). Originally it was an ancient track to a water mill and was probably busy with horse-drawn vehicles - the mill ceased in about 1850 and the track was never established for public vehicular access. But its wide because it must have been a very busy track 150 years ago. And it is bounded by ancient hedges/ditches each side.
You don't say what 'category' this right of way is and as I've said above there is no standard width. If you are concerned about it, you could try looking at the definitive map showing the public rights of way to see if it is accurately described. These maps are held by the County Council, or by the Unitary Authority for counties run by that system. I suspect you will find that it describes the route, but not the absolute width of the track. What problem is it giving other locals?