Virgin money transfer card rejected

Firstly check your credit scores on one of the free credit check companies rather than reapply straight away. Clearscore is very good if you ignore the ads! You should have got the card on the financials you have put above so it's worth checking there's nothing untoward on your credit record that you're not aware of.
In my experience it's only the Virgin rates that are worthwhile for stoozing on money transfer cards, so hopefully you can get one when you're able to reapply. However another option is to get the longest purchase 0% card you can, put all your day to day purchases, bills etc on it and then invest all the money you would otherwise have spent into whatever you were going to do with the Virgin money cash.
It's not as quick to make a profit as you have to build up the balance, but it works as well in the longer term and there is no initial fee to get the money.