Being of even greater vintage I understand where you're coming from! Are you leaving Plusnet for another phone company or do you need new SIM for another reason? I'm with 1pmobile which is cheapest by far for those with limited phone requirements, but I would think phone contracts are similar to broadband in that you pay in advance, so if your contract ends on say February 20 this month's payment will cover you until then. You should find contract details if you log into your PN account, maybe you have to give notice of quitting?
If unsure, best give PN a call as staff may not always monitor this forum. And don't cancel your direct debit just yet, this can lead to more problems.