Phone them up and cancel, say you need to reduce your bills but don’t really want to lose the features you have so will look for alternatives (I find if you just say you want to cut costs they mostly focus on reducing your package rather than discounts), alternatives can be streaming etc. so no need to lie and say Virgin.
Don’t agree to anything in the first call, just say it’s not enough of a discount and you wish to continue with the cancellation (usually you’ll only get a small discount offer + 12 month contract lock-in).
At that point it’s probably worth installing the Sky app, you’ll likely get a discount offer through that within a week or so (it’s 30 days before you actually lose the service), mine was 35% with no contract – I ignored it but apparently sometimes better offers come through.
A few days later I got a call from them asking if there’s any way they can change my mind, I asked for a 50% discount (for 12 months) with no contract lock-in and they agreed – I could have pushed it further (a mate got 50% off plus a £100 account credit) but I couldn’t be bothered. I wanted a Sky Q box for free to but apparently that’s a whole other department but might try that in 12 months time…