weird type of nuisance call

[#1]

I am getting a nuisance call every week or two at 2am-4am. When I answer there is silence.
What makes it unusual (for me at least), when I call the number on my mobile phone, it is instantly busy (any time of day or night)
When I call it from the land line it rings for a few seconds and then goes busy.
When I google the number it just says that it is a residential virgin media number (though clearly not being used for residential purposes)
I don't want to pay for call barring, don't see why I should pay a monthly fee to stop a nuisance call. Can I just get a single nuisance number blocked? And what are they doing to explain the ring/busy behaviour when I try to call back?

[#2]

Hi meem,
You can find a guide here regarding nuisance calls: http://www.plus.net/support/phone/nuisance_calls.shtml
Hope you find this helpful!

[#3]

If it's a Virgin Media number, it may be worth contacting them to see if they, in turn, will pass a message on to the subscriber.
We had a similar problem years ago, being rung up late at night by a modem, and when we called back, it was the modem again – no-one to complain to! Everything was BT back then, and a single call to their nuisance-calls bureau (whatever it was called) sorted the problem.
Good luck, anyway!