Problem SOLVED - hopefully but not totally satisfactorily !
I am replying to my own preoblem here because a 'nice man' from BT phoned me - from his home he said ( not sure why he told me that but he said he would also respond here when he got back to the office).
He reiterated what Ctarmey and others say above. YAHOO, who control btmail, have 'improved security' on their system. Two of these improvements affect me as a Mac user, with an Ipad and an Ipod :
1. I can only access my bt mail from one device at a time. If any other devices are linked to the server they will be shut off from the server. This arrangement applies even if the other devices are not switched on but are set to receive mail from the server by 'push'.
This could, for example, mean that if I go away for the weekend with my laptop I will not be able to access mail if my Ipad, sitting at home, is silently pushing for mail from the same server ... and a host of other undesirable scenarios.
SOLUTION : All devices which allow 'push' for email sghould be set instead to 'manual',
2. If I sign onto btwebmail I will be automatically signed off and need to sign in again within a couple of hours, even if I have checked the 'please leave me signed on' box. This, I'm told, is progress .....
SOLUTION : live with it .....
Like others here I am tempted, after close to 30 years of having a btemail address, to give up on them - especially as they have just, yet again, postponed laying firre optic supply to this city sentre location. (Virgin claim to have fibre optic capability at this address but on two occasions have sent installers who say it is not possible)