Our disabled friend cannot get to the phone in time before 1571 cuts in.
Is there any way the time can be extended to, say, over 30 seconds, or even 1 minute?
She did have an 'Ansafone' set to long delay but it died.

AFAIK, the BT version is a fixed delay (7 rings?).

As 1571 is such a rip-off anyway, why not revert to the separate answering machine? They're only £10 or so these days - or you might even get one for nothing on Freecycle.