Good luck suing a multi-billion pound company for an installation that's a day or so late. I'd expect any competent judge to dismiss such an action as vexatious and unmerited, and because it sounds like you've neither used VM's complaints process, nor the industry adjudication scheme that is the logical step after you've tried a formal complaint. It is an expectation in the courts that applicants have exhausted a company's processes first, and then used ADR options, with legal action a last resort.
Having an install date in writing is not a firm and enforceable guarantee (read the T&Cs), added to which there's automatic compensation for late installations - again something any judge should use as reason to dismiss a case.
Why not cancel under your cooling off rights? If you really want to sue over a one day late delivery, then I suspect you'd find the entire VM customer experience an ordeal, and whilst they'd never say it, VM might conclude that you'd be a better fit with another ISP.
