The talk talk mail is working (well mine is) and talk talk are not reporting any mail problems
http://broadband.talktalk.co.uk/outages
first thing is always to make sure you are trying to log into the correct place...
http://www.talktalk.co.uk/mail/
If you are in the correct place then A 500 error means (helpful error coming up!) "the server has encountered something unexpected stopping it from fulfilling the request"
So it could be anything.... if it only just happened I'd simply wait an hour or so and see if it comes back, if not you will probably have to contact talk talk.