It turns out that I'm not only the first person in this flat to want a landline, but the first person in the whole block - the other tennants all use mobile phones. But that shouldn't be a problem, the block itself should be wired up.
Ha. Ha. Ha.
Turns out that the builders fitted a DP and wired all the flats up to that, but then left the cable out of the DP in a heap on the floor. And they ran a couple of ducts in the cupboard, but a) they aren't the same colour as the ones underneath the BT manhole cover right outside which leads to b) the engineer has no idea where they go! The landlady doesn't know how the phones should be run, and the person who would know is on holiday. So the phone sockets in the flat are all wired up, but the cable between the flat and the exchange isn't connected and no-one knows where it should run!
With any luck BT'll send another engineer soon to sort out the ductwork (the one today didn't have the necessary equipment), and hopefully that one will manage to get it wired up.
At least at the end of this I should get an excellent broadband connection as the new flat is much closer to the exchange!