I’d say they were pretty generous when I applied recently - but I had no other credit card debt to speak of. If you’re definitely going this way, I’d also have a look at the MSE credit card club, then apply, then decide what you’re going to do - there’s no certainty until you’ve actually got the card.
Virgin does an eligibility check on their website as well, which I believe (can’t actually remember) shows you an “indicative” credit limit (“you could get x limit” or something like that)
They don’t like it because it costs them more in transaction fees. Last car I bought dealer wouldn’t allow more than £1k deposit on credit card. But it varies from dealer to dealer and some will be more amenable to threats to walk away from the deal than others.