Any court action would almost certainly cost tens of thousands (or, quite possibly, hundreds of thousands) of pounds. There's no legal aid available and there's no guarantee that you'd be able to get your expenses back if you won the court battle.
In practice, suing for libel (which includes slander) is only possible if you're either fairly rich or backed by an organisation with adequate funding (e.g. a teacher could call upon their union's legal team for assistance if, say, a parent was spreading rumours which could threaten their career).
Sometimes, however, the threat of legal action can be sufficient to gain a public apology (or, at least, to prevent the falsehoods being repeated). So it might be worth getting a solicitor to write a letter warning the relevant person that you're considering such action.
Chris