If UK house prices crash, will building society savings be safe?

I am aware of the Financial Services Compensation Scheme which should safeguard savings, but if building societies fail in large numbers, could this scheme cope with the resultant claims?

Consider that if house prices crash, when the market has reached its low point many of those with building society savings may wish to withdraw that money in order to enter the housing market. Would that be the final straw for building societies struggling to cope with the crash?