That's "free" as in "we, Virgin Media's management, think the muggles will be so fixated on the idea of something for nothing that they'll suck up a surprise £35 charge without squealing too much".
Raise a complaint using the online form in My Virgin Media, asking for them to accept your offer of a free settlement involving no costs to VM, but the credit of £35 to your account (after all, thirty five pounds = free, we've already established that). This is highly likely to be fobbed off, if that happens you reject the "resolution" VM offer and ask for a deadlock letter. With a deadlock letter you can then escalate the matter for free to the industry adjudication scheme, CISAS. Now that is free for you, in the ordinarily accepted sense of the word. But it won't be free for VM, nor even "free=£35", as they will get hit with some chunky adjudication fees.
Or the forum staff could intervene quickly and get the £35 cancelled or credited back to your account, thus saving everybody a lot of hassle?
