The problem appears to be older properties rather than flood plains.
Indeed. Taking Carlisle as an example, virtually all the properties which have been flooded were there when I lived in the city in the 1960's, many of them Edwardian or late Victorian. The first time these were flooded was in 2005 and many more have been flooded this year. Modern planners/architects can't be blamed for Carlisles ills. I don't know York well but it would appear that again is it is older properties near the centre which have been most affected