score:6
Answering my own question, as the result is useful. The reason I wanted to buy online was that VA used to charge an extra fee for phone bookings (not too sure if they still do) - and I wanted to avoid it.
I ended up calling Virgin Atlantic, who confirmed that this option is not available on their website and needs to be booked over the phone. They also would not charge a fee, because in this case phone booking is the only option. As an added bonus I found out that I actually had enough air miles to pay for the ticket - so the whole thing turned out to be much cheaper than I was prepared to pay.