Phone scam purporting to be from BT

I had a call this morning from someone purporting to be from BT Technical Support, warning me that unless I turned on my PC to deal with some infections, my router would be switched off in 2 hours time.  I asked the woman, who spoke with a South Asian accent from what felt like a long way away, for her name and number. She gave them as "Christine Wilson", on 03942629.

I said I'd call BT Technical Support should I encounter a problem (my internet contract is not with BT), to which she said it would be too late to deal with the issues once the router was off.

I called BT customer services on o1324452504 to report the scam, and they said it was the second such call they'd received today.

What felt different about this particular scam was the sense of urgency conveyed by the caller. When I said I'd call back, she kept asking "but when will you call?", repeating "warnings" that once the router was off, it would be too late.

I obviously didn't call 03942629, which BT confirmed is not a legitimate number.