The first of those links looks like new customer only pricing, and the company won't readily offer you that. The second link to My Upgrades and Offers is a very incomplete subset of all available deals, and usually offers paltry discounts. If you can't bear haglling and hate dealing with VM by phone, then the upgrades and offers links usually work, but won't be best value by a long chalk. I'd suggest as follows:
1. Do your research. Check out price comparison web sites like Uswitch for the cheapest comparable Openreach ISP package you'd consider - they will be discounted and offer good prices. Over an 18 month contract this is a circa £700-1,000 commitment, approach this with the diligence you'd use for making a purchase of that size.
2. Phone VM, and select options that will take you through to "retentions" who deal with cancellations. Know at the start of the call what you ideally want the price/bundle outcome to be, and also what you wuld settle for. You need to have these boundary values firmly fixed because you won't usually be able to negotiate a deal and leave it on the table whilst you consider it, that's not how the system works. The agent you are dealing with will be paid a bonus if they can retain you, but won't be paid the bonus if you end the call with "I'd like to think about that", and if you phone again the next agent doesn't have to offer you the same deal.
3. Explain that your current package is too expensive, and you hope they can help because you're seriously considering the offer from Company Z, and that's only £Y a month, and would save you £XXX over 18 months. Ignore any "throw ins" that you don't want such as (perhaps) a free SIM or a channel package you wouldn't have chosen, or a speed upgrade that you'll never make use of. Don't bother referring to VM's new customer prices or any personal perceptions of fairness, that doesn't count, all that counts is what those other companies will offer you, and the prospect that you might take your business elsewhere.
4. If you're going to accept the VM offer, get the agent to run through all important aspects including speed, any TV bundles (and channels important to you), any landline and landline add ons, and make sure the discount is for the full term of 18 months, so that all this should be recorded on VM's systems in case there's any problem later on.
5. If VM's best offer is still above your minimum and the Openreach alternatives are adequate, be prepared to say "no" and walk away and cancel. I always recommend to only cancel when a new Openreach line is installed and working, but some people prefer to try and avoid having an overlap. During your month's notice you might get an outbound retention call that's willing to offer you a stonkingly good deal, and if that happens then you can cancel the new connection before it is installed.
