I can't SEND e-mail from an account on my iPad 4, that CAN receive -mail

Question

Hi Again,
I am hoping someone on this forum will possibly have an answer to a very confusing problem.
I can't seem to get one of my e-mail accounts to be set up 'properly' on my iPad 4. The account in question is an account from BT, which has @btinternet.com at the end of it. I have 'installed' and deleted this account more than ten times. When setting up this account (as with all other accounts that DO work properly), the only info I am 'asked' to input is my name, e-mail address and password, in the 'text entry spaces' that relate to the INCOMING mail server. When this is done I USUALLY see the word 'verifying........' Then the 'blue tick marks' confirming that the info I have entered is correct. The validity of this info is also confirmed by the fact that this account can RECEIVE the e-mails sent to it.
Each of the last four or five times I have deleted this e-mail account and re-installed it I have NOT seen the word 'verifying.....' And I have NOT seen the aforementioned blue ticks. Selecting 'done' after re-entering my info just makes this settings box disappear, rather than show the verifying and the blue ticks, which then allows me to see that the account is 'properly' set up - or should be anyway.
Even so I still get all the e-mails again, but still cannot SEND, OR REPLY
The error message I get every single time I try to SEND, OR REPLY using this same e-mail account is:
'Cannot Send Mail'
'The username or password for SMTP: ***********@mail.btinternet.com is incorrect'
My username and password are NOT incorrect. The set up process does not even ask for a username or password for 'SMTP'!
Even if I go further into the settings for this account, I can find two spaces where I COULD put a username and password, for SMTP, but these spaces already have the words 'optional' in them so they are not supposed to be 'required'. Even if I DO put in these spaces my surname and password for this e-mail account it does not make any difference.
I have tried 'switching on' the 'other mail servers' which are shown below the 'Primary mail server' in another settings box, for the btinternet.com e-mail account settings, but this still does not stop the error message, AND the e-mail in question is then actually sent from one of the e-mail accounts connected with the 'other mail servers' - I know this because it appears in the 'sent' items folder of whichever account my iPad has decided to use at the time (not always the same one either). It also appears in the sent items folder of the account that I TRIED to use, despite the fact it was NOT sent from this account, and the error message said I cannot send mail (from this account).
I have contacted Apple Tech Support and they have told me that the problem is NOT with the iPad, it is with the 'account provider'. This is because they say that the info held and used by BT - the info that is used as the 'correct info', that is compared to what I have put in the set up boxes on my iPad - IS actually the info that is incorrect despite the fact that the info I use on my iPad and the info I use on the BT website (which was originally determined by ME when I first got my account) and is held by BT, is the info that is causing the problem of the error message. To put it another way, the info referred to in the error message is NOT incorrect, the error message is incorrectly generated.
Typically, BT have tried to deny the problem is caused by them because 'the info referred to' - which is my e-mail address and password - works correctly an ALL places that is supposed to work (on the BT website) AND works with the BT/iPad applications like BT Wi-Fi, BT Smart talk, etc. :( :( :(
Any help or advice that anyone could give will be very greatly appreciated
Many thanks
Bob

Answer 1

Update to above question:
Hello All,
To anyone with the same problem described above, on THEIR iPad (if it is running iOS 7.0.2):
Go to Settings; Mail, Contacts, Calendars; DELETE your *******@btinternet.com e-mail account, that you originally set up either using 'Other', or the 'BT' option which I am sure was in the list previous to the iOS 7 update.
Then ADD a NEW account choosing YAHOO from the list of options. DO NOT USE 'OTHER'.
Enter the correct details just as you (almost certainly) had already done in your previous attempts using 'other'.
When you see the 'verifying......' and 'the blue ticks' you should be able to exit settings and open your mail app and then receive all your 'old' e-mails again, AND be able to SEND as well.
All my 'old' e-mails, were NOT found in the 'old e-mail' folder though. THEY are still in my inbox.
So this fix worked for me.
After I deleted my account from 'OTHER' and put it in Yahoo, I like other people also ended up with more folders.
I hope this works for you on YOUR Apple devices.
Bob