Hi Brian,
Sorry for not replying yesterday but I had just about had enough, thought I had found the problem, but too late to solve it.
Firstly I "uninstalled" our two accounts in the way you instructed. Then set them up as POP accounts copying all settings exactly from laptop.
This worked for me but not for my wife's account. Ah ha I thought, I just wonder when I set up laptop Mail (6 years ago) if I had to use a different password for my wife. Too late to talk to the ISP last night but I did so this morning and that was the problem!
So thanks for your help BUT one other bit of advice please. Our two accounts each has it's own separate Inbox, set up automatically I guess on the ISP server as well as on my computer. However there is only one Sent box which contains the sent emails of both my wife and I. The ISP guy (who had an iPad and was quite helpful), said he was sure I could set up two Sent boxes by changing the Mail settings but could not tell me exactly where. I managed to do it 6 years ago for my laptop but be blowed if I can find how to do it now!!
Any guidance would be appreciated!