Council's don't have free money, they only have what they take from the local population and businesses by force.
It's absolutely right that the individual should pay for the actions of the individual.
As for the £700 bill, depending on how much damage there was to the fitting etc, how many man hours were taken to fix it and so on, it's not that unreasonable.
My point is if they can charge £70+ for a parking offence etc ontop of the money they get from taxes, why shouldn't they have a decent buffer of funds to replace damaged road infrastructure as a result of poor weather conditions.
If they had upheld their job of spending that money on making the road safe (gritting/ploughing/filling holes etc) and fit for purpose, then the OP wouldn't have necessarily been the position he is in now and their wouldn't be a sum of £700 to find from somewhere.
For example, if you drive over a pothole, you shouldn't expected to pay for all the damages to your tyres as the road was unfit for purpose.