If you want a good deal, then you need leverage. And the only time you have leverage as an existing customer is when all three of the following apply:
a) You are in a position to leave (near end of fixed term contract or out of fixed term contract)
b) You are in possession of market knowledge - better offers for similar bundles from competitors (eg via Uswitch or other PCW)
c) You are on the phone to retentions, playing the game, and the agent believes you are serious about leaving.
Know at the start of the call what you can get from competitors, what ideal outcome you want from VM, and what you will settle for. I suggest you have these two boundaries written down in front of you. You need to have these boundary values firmly fixed because as you've already found you can't 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 probably 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 the next agent you speak to isn't interested in what you were offered before. If anything, coming back to the table after mulling it over will suggest to them that you're more committed to VM than before and don't need to be offered such a good deal.
Ignore the history and previous offers. They're gone, but that doesn't mean you can't get a stonkingly good deal with some effort. 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. See what they say. Usually they won't price match, particularly on first offer. Your response to their first offer will almost certainly need to be "thanks but that's still not enough, it is nowhere near Company Z's price, I'd rather the £NNN difference over 18 months was in my pocket not Virgin Media's". You may then have to endure the charade of "need to speak to my manager" when in fact they're just going for a coffee or handling another call, since the agents have plenty of leeway. Ignore any package "throw ins" that you don't want such as (perhaps) a free SIM, speed upgrade or a channel package you wouldn't have chosen. Remember that in the discussion, appealing to loyalty or fairness are utterly pointless - those count for nothing, and the agent is doing their job when trying to keep you as a customer at the highest possible price, you are showing that you can get a much better deal elsewhere, and you WILL take that competitor offer if VM can't come up with a great counter-offer.
If you're going to accept the VM offer, this will be a new 18 month contract, 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, so that this should be recorded on VM's systems in case there's any problem later on. If you accept an offer, then check the contract email you get carefully - there are a few instances every month of customers agreeing a deal and then finding that what's been put through has important differences, almost always in the company's favour.
If the Openreach alternatives are adequate, and VM's best offer is still above your minimum, be prepared to say "no" and walk away and cancel (but only cancel when the Openreach line is installed and working). Remember that the retention agents do their job all day every day, and unless you're a procurement professional by trade, they are far more experienced than you or I will ever be, and they get regular training to spot who is likely to leave, and who is just bluffing. If you are not prepared to leave they'll spot that, and know they don't have to offer a good deal, and I'll wager that they are either incentivised to retain at minimum discounts, or simply shown the door if they give too much away.
You might subsequently get an outbound retention call in the last few days of your contract after serving notice that offers the sort of deal you'd stay for. Do not rely on that happening. If you do cancel and the call arrives, then give it thought because the same rules apply: Know your price/bundle limit, and the deal is only valid when offered.
