Hi JS.
If you switch to Virgin you don't need a BT line because Virgin runs through cable not the BT exchange. That's how you can drop the BT line rental - cancel your BT line. Beware though, if you ever intend to use anyone other Virgin in the future you will have to pay whatever BT charges as a reconnection fee at that time.
Before you do make the switch though, have you looked at offers from other providers such as Sky? Yes you'll still have to pay BT line rental but the rest of the Sky package is much cheaper than my Virgin services. The service from Virgin is pretty good (I've been with them/Telewest for 4 years) if you're looking for fast broadband, etc, but their packages are normally more expensive than many other equivalent packages on the market because of that.
For example, my current Virgin package is nearly twice what I'd be paying if I was with Sky. The problem for me is that I'll currently have to pay a BT connection fee of approx £125 and (I think) stay with BT for 12 months before switching to Sky. The other downside is that Virgin are going to increase my broadband speed from 4MB to 10MB whereas the fastest I could get through Sky (BT exchange) is about 4.5MB in this area. But I could live with that for £20 per month less considering that's roughly what I'm getting now.
So my advice is not to switch to Virgin unless you are really after fast broadband. Others may disagree - this is my first post on here so please be gentle!
Reel