Hi Parsnips and welcome... where do you live in UK? We are happily harvesting our parsnips now after weeks and weeks or frost and snow.

Usually this is caused by them getting too old and they are like this before they are going to flower in the second year. It could also be caused by dry conditions.
You could try growing smaller roots by leaving them closer together when you thin them out, as the small roots are usually sweeter.
While the core of the root may have gone woody, the outside should still be fairly edible. Have you tried just cutting off and cooking the outside parts for this year.

I remember my mother cutting up very large parsnips and removing the inner core, we never seem to ened to even though we have pretty large parsnips.