The online offers are a tiny subset of what's available - VM never have and apparently never will allow customers to manage their contracts online, and the whole customer experience is built around 1990's style call centre sweatshops, with crummy IVR before you get that far.
If you want to renegotiate, you have to phone, up select options for thinking of leaving, and if they won't match or beat the deal you would otherwise take, then you cancel, although recent reports suggest that VM are making that as difficult as they know how. At some point you will probably be speaking to UK based retentions staff (although they may not be highly motivated at the moment) and they're your best chance of a decent deal. General opinion is that phone first thing in the morning improves your chances of getting a UK agent, but I don't know if that's truly the case. Offshore agents seem to have less leeway to offer good deals. Because of the way retention agent incentives work, the deals they will offer can vary day to day, agent to agent, there are no firm rules here. If they won't strike a deal you can accept, and you do cancel, there's a good chance of you getting an outbound retentions call during your notice period, and those staff are usually able to offer discounts equivalent to new customer pricing. There is no guarantee on that call happening, or coming at a time when you can take it, so don't make that a central part of your strategy.
If negotiating, avoid mentioning fairness or loyalty, those count for nothing and will suggest to the agent that you're easy meat for the win-back script based around VM's speed advantage, or by throwing in low cost giveaways like a VM sim. All that matters for you is that the agent believes you will leave, that you know what offers are on the market, and that within their bonus calculations they can find the leeway to achieve the necessary discount. Quote the lowest comparable price you can find (even from a company you might not touch with a bargepole), and quote it early in the call - the agent gets bonus on number of customer retained, and therefore for them personally, time is money, as soon as you're off the phone they can be onto another call. So if you give them sight of the goal early, they can wrap up the call quickly - either you get the deal and everybody is happy, or they say "computer says no" and at least you know where you stand without (hopefully) twenty minutes of tedious pretend back and forth with "need to speak to my boss" lies from time to time.
