Just ignore the car voucher that Virgin gives you and book a car with someone else including insurance and gold cover if you want more than I driver. Have done this several times on Virigin and BA holiday and was even advised to do this by a
travel agent once.
Several companies give good rates. Some I had used are below.
usrentacar.co.uk (best rates and then choose which company to use, Alamo, Dollar or Budget)
airlinenetwork.co.uk (tends to be Dollar only)
hertz.co.uk (some people get good rates from them)
I tend to only use usrentacar as they have been cheapest for me. At Orlando I prefer Alamo purely because you get to choose your own car and then you can check out boot sizes and extras in the car as to what you prefer as well as colour (purely a woman thing).
Ignore all the crap that the rental car counter guys try to sell you and just say no thanks I just want the car I booked. It is annoying but they all do it to earn more commission I guess.