You have no choice. Facebook is now forcing mobile authentication. You can't access your account or deactivate your account unless you provide them with your number. They seem to be slowly rolling this out to users. I did a google about this a while back when I got the message, seems like quite a few people have encountered it and couldn't do anything about it.
It's so wrong! I don't know if it's possible to make an official complaint about this to Ofcom or something? They shouldn't be allowed to do this.
I haven't encountered that, but I really hope I don't because I don't have a mobile.