Local trading standards gave us the correct BT number to report it to - BT have blocked that number from calling our line though i suspect they’ll Use a different number another time.
Correct. Mostly these scammers use VoIP services (Voice over Internet) where getting a new outbound number is likely to be trivially cheap and easy, and doable within a matter of hours or minutes. Unfortunately this means that blocking individual numbers has little effect.
There are some very interesting YouTube channels which demonstrate what these people will do if you participate. The common reason is to convince you that there is a problem with your computer that requires fixing. This usually involves some kind of scaremongering with references being made to viruses and hackers (which of course are fictional). This may involve using legitimate features, such as the Windows eventviewer and task manager utilities, to overwhelm the victim with scary "techy"-looking information and ultimately mislead them.
Of course, once you have been convinced of this it can be used as a means to extort money from you to "fix the problem" (read: do absolutely nothing), which can be in the hundreds or thousands of pounds. If the victim refuses to pay the scammers may start to cause actual damage (such as deleting files), which may either be attributed to the fake "viruses" or "hackers", or used as a form of blackmail.
Of course, it can be much worse than this. Some scammers simply want access to the computer to steal private files or even to install an actual piece of malware. However most often they seem to be in it purely for the money.
The Youtube channel which is particularly informative is Jim Browning <
https://www.youtube.com/channel/UCBNG0osIBAprVcZZ3ic84vw>, while some others, such as Kitboga, take a more entertainment-focussed path by finding amusing ways to waste the scammers' time <
https://www.youtube.com/channel/UCm22FAXZMw1BaWeFszZxUKw>