sounds like its along the lines of the microsoft scams.
they will find a way of showing you your pc has a virus, usually by proving your PC has a perfectly innocent folder.
Then they will ask you to allow them remote access to your PC by going to a wesbite and then charge you for removing said virus.
Plus, whilst they have access to your PC they may be removing information for it.
never trust any of these calls. BT/ broadband companies and certainly not microsoft would never care about your PC and what its speed is etc.