It doesn't look like cat-facing or a pollination problem. I have had examples of that problem over the years and that distortion looks quite different. My funny strawberries don't have any pinched areas, they are fully pollinated, plump, tender and delicious.
Having done a bit more research it looks like this is an example of fasciation - http://strawberryplants.org/2010/12/deformed-strawberries/ . This seems to be caused by cold dry conditions in the Autumn which is a reasonable explanation as I keep them in a cold greenhouse which doesn't see any Sun from October onwards. I also tend to keep the greenhouse dry after the growing season is over. I initially suspected virus problems because I have let these propagate for at least the last 15 years.