I saw a thread recently (
'Support onclick'? - MoneySavingExpert.com Forums) about this sort of thing.
Company was called Support On Click from India. Their phone operators were not keen to give their location and claimed to be UK based.
In a cold call, they would say that there was a problem with your PC (I suppose most homes have one these days) and then talk you through demonstrating the infection and setting up remote access to your PC. And charging monthly too.
One interesting snippet is that when challenged, calls were routed to a senior individual who tended to threaten and swear...