You can wear all the PPE you like, but the fact is you'd be operating a chainsaw in a public place, a public road no less, you're into working on the highway/road closure legislation, public liability ins and no doubt a whole ruck of elf & safetly bollix, before you look at permissions. It'd come under the same legislation if you wanted to trim hedges on a busy shopping highstreet, just the odds of getting caught are different :lol: I carry a silky for those awkward branches, great little saws.
to the OP, the reality is that if you plan a day out on the lanes pretty much anywhere in the UK, you are going to come across overgrown lanes. The real question is not about weather you're allowed to trim a few bushes back, it's about do you want to spend your day driving or hedge trimming? because the day ain't long enough for both!
If you join a group who go out regularly you have a much higher chance of having someone in the group with local knowledge so you can aviod the scratchy lanes, but even then you'll drive a new lane for 2 miles down a awkward narrow lane and discover it overgrown at that point for the next 1/2 mile, do you reverse the 2 miles to avoid scratches, spend the rest of the week hedge trimming, or go for it?
Maybe you could research your laning days via google earth to try to spot any problems on your planned route, but I think scratchy is par for the course in this hobby.
Vinal wrapping to protect the paint?