Unless there's something in consumer legislation about change of mind, and I don't think there is anything that would be specific to this case, I think you're obliged to pay the 12 month contract (or 10 months to be exact, considering they're giving you two months free).
That said, I'm presuming you agreed to the new 12 month contract over the telephone while onto their contact centre, because generally speaking those calls are recorded. I think the call recordings would be proof enough to you agreeing to the new contract, and they don't need a signature. If it was face to face in a 3shop or something like that, they would have a harder time proving that you accepted the new terms, but based on your post it looks like that the 3 staff you spoke to were already aware of this.