No, I’m sorry but you have already spoken with the ‘correct team’ ie retentions and they will do nothing (was you have found out) until closer to the point where you might actually leave for another supplier. They know that you probably won’t do it now as that will cost you early disconnection fees, so they will spin it out.
Alas, no you can’t challenge the disconnection fee on the grounds of a few outages, outages are a simple fact of life, they happen. Were this disconnections long enough to trigger some compensation payments, basically they need to be at least two full working days? If so did you get the compensation?
"If I wait can I guarantee a favourable deal to what I'm paying at present?"
Absolutely not, any deal is likely to be somewhere between what you are paying now and what a new customer price is.
"U Switch currently offer 250 meg with Virgin for a penny under 24 pounds a month so there are deals out there."
Yes there are, but these are ‘new customer’ pricing, you aren’t a new customer, so you won’t be eligible for them!
"I should stress I'm happy to stay with Virgin. But Be Fibres offer (and Sky's) are superior."
OK yes I do get it, changing is inconvenient and requires effort, but VM know this, why would they match another provider’s pricing if they think or suspect that you are unwilling to leave because of the inconvenience? If another provider’s offering is ‘superior’ then why not go with them?
I’m sorry and it does sound critical, but inertia and ‘can’t be bothered to put the work in’ are real things, VM knows this, frankly, every supplier knows this and counts on it.
You asked about ‘who you can call to negotiate with’, but tell me, what is your negotiating position? Do you have one? Are you actually. really prepared to leave? And can you convince VM that you will and go elsewhere?
"Be Fibre come a knocking claiming 900 Meg for £29 a month and offering to pay the remainder of my contract."
So what are you waiting for? Leave now, it’s an obviously better deal for you; unless it isn't true and Be won’t actually pay off the rest of your contract - do be aware that any doorstep salesperson will promise the earth to, well, get a sale chalked up and get their commission.
Look, bottom line, you will absolutely not get a spectacularly good deal from VM, unless and until you actually leave; put your notice in. Otherwise they will simply call your bluff, their opinion will be that you won't leave, you can’t be bothered to put the work in - and this actually works for the majority of customers. They simply assume that you will fold, they can't tell if you are the exception to the rule!
This is the reality of the situation; the question is this, what are YOU going to do about it?