I can't quite get my heard around this. My landline doesn't work so assumed it was the phoneline, which would therefore affect the broadband.
But the broadband is working fine.
I've plugged in a different phone, and that doesn't work either at my house, but have checked that it does work ok elsewhere. So I'm a bit stumped, but loathing the idea of phoning Orange, as it was so tortuous last time.
Is this a logical problem to have, or am I right to think it doesn't make sense?

If you have An NTE5 type master socket then remove the faceplate and connect the phone to the test socket without a filter. If it still does not work you have some sort of line fault.
Be careful removing the faceplate if you have phone extensions as it will have wiring connected to the back of it, just remove it enough to expose the test socket.

It is perfectly possible for the broadband to work but the voice side of the line not to, or vice versa. It could be the equipment the line is connected to in the exchange. The two parts, broadband and voice are split off to two different sets of kit. So it is entirely possible for one of those to fail without affecting the other,

There are also certain line faults that can prevent the 50V DC signal that is present on the line getting through so the phones in your home stop working. But they can let through the broadband signal, though often somewhat degraded compared to a fully working line.

If the test socket also does not work then the fault is likely to be the line so get on to whoever you pay line rental to. But just be aware if the fault is not on the phone network you could be charged a call out fee. Also the Openreach engineer who attends to investigate the fault may not fix any faults with your internal wiring or phones.

So if you do have the right type of master socket it is important you use the test socket as that is connected directly across the line and all your extension wiring is isolated so does not affect the tests you make.