It seems that my hope of it just being the inner tubes was a bit too optimistic. On closer examination my rear wheel now has a buckle and the front tyre has what looks like a chunk taken out of it.

I am reporting the pothole to the council (although its possible this has been resolved) in order to follow the process for making a claim, as I don’t wish to be down on the cost of a new rim (or potentially wheel) and tyre. I will also take the bike into the shop to have a proper assessement in case there is any more damage that I am missing.