As you've relatively recently joined you'll be locked into an 18 month minimum term contract with exit penalties likely to be £240.
Given your customer experience you may have a case for demanding to be released without penalty, but you'll need to clearly state a good case that demonstrates that the service has been nowhere near what might reasonably be expected, and that VM have failed to resolve the matter despite having the opportunity, or that multiple poorly handled problems represent an overall failure of service quality. To achieve a penalty free exit, you will probably need to steer this through VM's complaint process, and very probably escalate to the industry complaints scheme, CISAS (not forgetting a copy of any CISAS complaint to Ofcom). Sometimes forum staff can intercede and arrange for customers to be released without penalty to avoid what for the company is an expensive hassle, and if they offer that it is your quickest resolution.
If you choose to do this, the grounds of your complaint is the poor performance and the poor customer service, and your request for release from contract without penalty is twofold: First the Consumer Rights Act 2015 that requires any consumer service to be provided with "reasonable skill and care", and second, the Ofcom Fairness Commitments which VM signed up to in 2019, that state "Customers’ services work as promised, reliably over time. If things go wrong providers give a prompt response to fix problems and take appropriate action to help their customers, which may include providing compensation where relevant. If providers can’t fix problems with core services they have promised to deliver within a reasonable period, customers can walk away from their contract with no penalty."
Make the complaint using the online form in My Virgin Media (as you've found, VM aren't capable of communicating by telephone), summarising the background, stating that grounds above, and requesting a resolution of either (1) immediate release from contract without early termination fees, or (2) if VM will not agree to that, the issue of a "deadlock letter" for the purposes of immediate escalation to CISAS. If escalating to CISAS you will need to provide the most detailed explanation and history possible (don't forget that they start off knowing nothing about your case), detail and rudeness, disconnected calls, long wait times, incorrect advice, broken promises, and you should set as your requested resolution release from contract without penalty, plus compensation for the poor connection, and the poor customer support. VM's handling of formal complaints is conducted to the same exceptional standards as their customer service, so don't expect too much from that, but sometimes they'll see sense, more often than not they'll reject your complaint or fob it off, but that doesn't stop you from escalating to CISAS.
When and if it gets to CISAS, the complaint is reviewed by a trained dispute adjudicator, and they offer you what they believe is a fair settlement, if you accept that then it is binding on VM. Of the broadband complaints to CISAS, data shows that VM immediately concede on 42%, they challenge the remainder, but lose 50%, and only 8% of CISAS complaints are found in the company's favour. That, unsurprisingly, is the worst performance in the industry, tieing with Post Office broadband for bottom place, which tops off the company's recent achievements in customer service.
As a regular in this forum, I find it dispiriting to be offering advice like this. VM's customer service is appalling, it has always been appalling since it was offshored to some third world dump (and outsourced to TheOffshoreCompanyThatDoesn'tGiveATinker'sCuss Ltd), yet the bread-heads of VM's US parent company Liberty Global and VM's useless British management have proven time and again that there is nothing of such poor quality and cheapness that it can't be done still worse and cheaper.
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