Hey @
Lawrenced - welcome to the RAC Community and thanks for making your first post!
These situations can definitely feel awkward and definitely spark debate about how best to handle them. Sometimes it can work smoothly and flawlessly by going directly to the other party's insurance company - however, as you are unfortunately finding out, it can be hard work. My recommendation would be to get your own insurance company back on the case. I'm assuming you have the registration number of their vehicle? And your witness that gave you the image - have you also got their details - would they be able to provide a witness statement to your insurer?
Assuming everything goes through smoothly, if you have an excess to pay, your insurers will claim it back from the other party - some insurers don't even charge it for cut and dry cases where liability is not in dispute. You could tell your insurers to not progress your repairs etc until liability is resolved and accepted by the other party if you are able to as well. But the first thing would be to get them involved now - they will no doubt have a greater impact in sparking something from them than you as an individual can.
Hope that helps,
Nick