I wonder if your previous provider released any personal details?
It is no doubt a scam call that you received.
What should be of concern is how the scammers got hold of your personal details and in particular if they had details exclusive to BT such as your BT account number or other information that is not easily obtainable except from BT.
There are a number of threads on the forum regarding this. I suggest that you have a read through them.
If you feel that information you have supplied to BT has been compromised you should report it to the Information Commissioner.
If the scammers did access your computer, if you have not already done it you should change all your passwords for all accounts, banking, email etc. Do not use the computer that the scammers accessed to do that.
Check your email accounts to ensure that no forwarding email addresses have been set up which could forward anything to the scammers.
You should also run a malware and anti virus scan on the computer and check for any software that may have been installed when the scammers had access.
I would disconnect the computer from the Internet until you have done all that.
You should also inform your bank etc that your account may have been compromised and ask them to keep an eye on it for unusual transactions.
Reporting this to Action Fraud is pretty much a waste of time. They will not investigate it. All they will do is collate the information and may pass it onto your local Police Force.
If your bank accounts have been compromised and monies stolen you should report it to your local Police.