do some research on smart repairers and get some additional opinions, that has to be a better option than a new roof.
3 out of 3 have said it's too bad to be repaired with the smart dent repair methods. Was a a right pain to hear that as I was initially relived when I saw the damage as I didn't think it was too bad and would be easier to repair than replacing the roof panel
Apparently the roof panel is spot welded into place, that gets taken out and replaced with a new panel. Obviously all the headlining with all the lights and anything else in the way needs to be removed
put in a freedom of information request on when the trees on that stretch of road were last inspected and the schedule of inspections. I hope you have photos of the offending tree and branch etc. too. I doubt they inspect them regularly which will really help your case.
I personally would make sure I'm not out of pocket for something that wasn't your fault. If it was (for instance) a neighbour and their roof tiles came off and landed on your car, they would be liable, so I don't see why the highways agency shouldn't be. Stick at it and I'm sure you'll get it sorted.
If you need someone to email high up, try here... https://www.gov.uk/government/organisations/highways-england
I have a camera so caught it falling on video
I emailed the council and highways england. The council initially confirmed it was their tree and refereed me to their legal department. Then I got an email from them which said I was misinformed and the fault lies on Highways England. Great shout on the freedom of information request though. Bet that will take months to get a reply but collecting as much evidence as possible is vital. Exactly! If it was a neighbours tree they will be liable. But because it's the council/Highways I imagine them doing the same as they did with the pothole claim. They will just say 'it was never reported so as we didn't know we aren't at fault and no chance to stop it". If the tree was shorter it wouldn't have happened, but they pretty much never trim trees unless large branches look dangerous.
If I get it repaired through insurance they're likely to just say as it has been repaired it counts as the problem being solved. But I lose 4 years off my no claims and my price will go up a little. I heard this (but not sure if it's true), apparently if the total the insurance paid for the repairs is payed back to them they wipe the claim and you get your no claims back. No idea how true that is but I can't imagine getting anywhere near £3k from the Highways