Now wishing to take on Ethel who has been consistently right,
If A refuses to pay the whole of the claim then B can go after C for the difference and this is [commonly] done for the loss of the no claims bonus in the UK. Clearly B has to have a cause of action against c - usually but need not be - negligence and can't say 'he damaged me' - I think that is Letang v Cooper. The right to sue - is it prorogation? is not given up under that 1838 case (Preston) if they dont pay the whole amount.
And yes B can go after A for breach of contract - but not recover the same amount of money from both. Although Denning is now dead - he was in the forefront of not allowing insured parties - this is the insurance co here - evade liability and impose it on uninsured parties - that would be B or possibly C here. Kinda made sense but judges are much more afraid for their PENSIONS nowadays and run like frightened rats when the govt says Boo!
erm that's about it.
PP