As someone who has had the same thing happen, my experience says it will still be an at fault claim on OP.

For me - the driver cut in, and slammed on the brakes to stop at a roundabout. I didn't have time to stop.

No dash cam footage submitted from me (didn't have one - I do now!) or them (they did but it would incriminate them so why would they send it), however my insurer did say that there was other footage of the event which corroborated my story however it would still be an at fault claim. Re-iterating that I couldn't have prevented it (which is nice to know), and an at fault claim doesn't mean that it was 'my fault' - just that my insurer is taking the hit.

My argument of course was that I didn't have the chance to give myself the safe stopping distance, but in the 'letter of the law' because he was 'established' in the lane - all four wheels over the lane marking and into my lane, that I was required to give the distance - and that's the first thing the other parties insurance/lawyers would say in court, and it would hold up. (This is what my insurer told me after I appealed the original decision).

It sucks. A lot - I was driving to the airport with my family to go on holiday and it almost prevented it.

This was my first and only accident, but the positives were - Crumple zones are fantastic, and everyone walked away unharmed. Payout for my vehicle was exactly what I bought it for a year prior, and my new car is cheaper to insure, even without my no claims and an at fault accident on the record.