Not many of them down here. I'd still have a go thoOr, even worse, a wanna-be medico with legal pretensions! Back in the real world, , reclassification of a road is remarkably rare, very time consuming and not in the least bit cheap, so it doesn't often happen off a private bat.
This matter can be sorted fairly simply in re the trees, the roof is a different matter. I think it makes more sense to dwell only upon the trees on the other side of the road to the house, shave them right back and top as necessary.
It's been raised with the council, they have a statutory duty to maintain highways, they have to do it - if they don't, get a Court Order, if the council don't do the necessary* they will be in contempt. This is a cheap / economical way of doing things since, once a Court Order has been attained, there are not really any further costs to the OP. In fact, if he can read and write and follow basic instructions, there is no reason why he need seek professional assistance to gain one.
*The chance of a council ignoring a Court Order is vanishingly small, so this is a good way to go.