It is easy, I did it all the time when working in debt collection for a public utility.
Ring the number, pretend to be a BT engineer, ask if the line is ok and not crackly, say there have been faults reported on same exchange.
Say they will lose the service for 24 hours unless an engineer replaced their inside box, COULD YOU CONFIRM YOUR ADDRESS PLEASE OUR ENGINEER CANNOT FIND YOU. Simple
A few years ago there was a spate of people ringing saying they were GPO engineers, and telling the answerer that their phone was dangerous. For their own safety they had to put the handset in a bowl of water.
The GPO then had angry calls from people saying when were they going to be sent replacements for their ruined phones.
i agree wiv CheekyChops - google the phone number - if someone has advertised cars or whatever else - say on autotrader, ebay etc or any other forum, it brings up all relevant info used on that number