I,ve just lifted my late crop of Dessiree potatoes and there are brown marks all through the tattie ,any idea what could be the cause of this?

It would help if you could indicate where you live on your profile. We can't tell for sure without a photo, but many have been reporting potato scab this summer. Here is some info:
http://vegetablemdonline.ppath...

Some possibilities are illustrated on this page, does it look like any of these?

http://www.extension.umn.edu/g...