The VM network uses amplifiers and one of those will be what the new cabinet is to house, specifically a line extender
VM set different levels of amplification and attenuation on their network to balance signals out. If your signal is too weak or too strong it will cause problems, and their power budget appears to indicate you're too far away for a reliable service.
The maximum cable length from the green cabinet depends on the settings in that green cabinet, there is no right or wrong answer, and in your case Virgin think that the extra 20 metres is too much.
VM aren't going to connect you if you install your own cable to their network, they're more likely to prosecute you, harsh as it is!
Try and escalate it within Virgin and see if they'll look at it again, they may have gotten the numbers wrong the first time around, but if they are right you are out of luck. They can install a lower loss, higher grade cable which can extend the reach but if that's already being used on the properties near you it's problematic.
Lastly, VM have a budget of 300GBP per new home connected. It sounds an awful lot like whichever way it goes your costs would come in way above that and, just as BT have their commercial viability levels, VM do too.
Sorry I can't be more positive