Do you have a specific vehicle in mind or are you referring to normal traffic?
Well, that was a pretty frustrating couple of hours.
I cannot find any statutory duty in respect of the local authority maintaining or contributing to walls abutting the highway save for their ability to repair a retaining wall that may present a danger to passers by as a matter of urgency and recover the cost from the landowner.
There is not a case I can find that supports a claim in tort and I have combed Practical Law which is the usual source for such information.
The case I was thinking of related primarily to flooding
I know local authorities have contributed to the upkeep of such walls where the property is listed or of interest but this seems to be done either by voluntary contribution or some sort of local grant scheme.
The bot***** *****ne is that you may be able to claim on your insurance and that's pretty much it.