most normal DVD recorders... and DVD Recorders with hard drives too. Given the medium term reliability of DVD Recorders you might be as well choosing something cheap.
What won't work is Freeview PVRs and Freesat PVRs. They don't record from an external source; only from their own TV/Satellite tuner.
If you want to record from Virgin using a simple point & click from Virgin's schedule then you really need to bite the bullet and go for the V+ service. That sort of integration isn't available on a 3rd party recorder IFAIK. It's a similar story with Sky.
You can set reminders on Sky, and then set the DVD recorder to record it's AV input for an ovelapping time. It's not the best solution, but short of paying for the extra recording functionality as part of a step-up package (Sky+ recording now free with Sky, but chargeable on Virgin???) then I don't believe there are many alternatives.