I have the exact same issue, took out the Big package which the website stated would include Sky One & BT Sports however this was not included when the box arrived. I called Virgin and they advised I would need to pay extra for these channels even though the website stated otherwise. False advertising.
Went through customer services by phone and messaging but they would not listen and only keep repeating that the HD channels were not included. I finally got so frustrated and angry that I have not received what they advertised , that I took the advice of another poster who suggested that I contact retentions and see would they would do if I said that I would be leaving Virgin as they have failed to provide what was advertised and had therefore broken the contract. I did that and at least I finally got to speak to someone who knew what they were talking about ! Retentions finally agreed that their website was misleading for the bundle that I had purchased and added on the HD channels at no extra cost. However, I have just received an email showing my bill has increased to include an extra charge for the HD channels so I don’t know if this is yet another mistake or they are trying it on again ! I have only been with Virgin for one week and I must say that they have been the most difficult provider that I have dealt with . From what I have been told, it appears that Virgin have been taking channels off some packages but have not shown these variants on their website so it has mislead a lot of new customers. As you have said, false advertising.