Hi @Mike0070, thanks for your post although I'm sorry to hear you received this call.
I'm guessing a lot of information has been removed from your post, due to our Moderators noticing that you've provided some of your personal details in a public thread.
However, I can say with certainty that Virgin Media does not call up non-existing customers (or even existing ones) and asks them to download Teamviewer.
Teamviewer is an app that allows the user to gain remote access of a device such as your laptop for example, and scammers use this to try and hack into your personal details.
I'm unsure how far you got with allowing them into your personal devices, but I'd recommend running an anti-virus software scan throughout those affected, just in case!
I'd also recommend viewing this link for further support on dealing with fraduluent calls.
I hope this helps