White rotting spuds

Hi,
Can anyone suggest what is up with my pink fir apples. Two weeks ago I cut down the haulms as nearby toms got blight although there was no obvious sign on the spuds but as the haulms were pretty ragged anyway I decided to play safe. However on digging up the tubers under some plants I have found a number of spuds whose flesh has liquified or is in the process of liquifying. I initially thought blight but the weird thing is that the liquified goo is really bright white, whiter than healthy spuds. There is no sign of brown discolouration which I believed was always present on blighted tubers. There is also a foul pong with some but not all rotten tubers
So far of 4 plants dug up 2 have had manky spuds with one having about 1/3  diseased while for the second only 6 showed disease.
Can anyone advise as to what this might be, what effect it will have on storage and should I pull the rest of the spuds asap.
Many thanks
Jon

I only grew PFA the once, and I don't think I had blight, but quite a few did go mushy in the ground.  Don't know if this is simply a common problem if you don't dig them up sooner?

Sadly I don't think it is being let in by slugs as some spuds appear intact but are like bags of goo. Plus I do have some slug damaged spuds that appear to not have any sign of rot. I have pulled the remaining spuds and there appears to be less frequency of bad spuds along the row but they are still present  .