Hello,Customer and thanks for your question.
If you are moving into this flat as a new tenant, it shouldn't be necessary to know who the phone provider is, especially if you want to change it. The new bill can't be in your name, until you officially change it over, and when you call to subscribe to any phone provider, they should be able to tell you whose line it is when your new one is installed.
If you call various other companies, beside BT, to find out who the line is with, giving the phone number might be sufficient, OR call BT and ask if they know which company would assign a phone number like the one you have, unless, as it is in the USA, you're able to 'port over' your own number when you change providers.
This should help:
"Who can supply a phone service
It is now possible to choose between a range of phone service providers for phone lines and equipment providers for telephone handsets, faxes and switchboards. As well as BT, other phone service providers now include NTL (incorporating Cable and Wireless plc) and Energis Communications (for business customers only), and various cable phone service companies." (see more, at: http://www.adviceguide.org.uk/index/your_world/communications/phone_services.htm
And this, as well:
I wish you much good luck, in solving this mystery, and then choosing the best provider for your needs.