The first thing to do when it happens is check to see if you can log on to your email account via a web browser. If you can there is obviously nothing wrong with your password or account.
In your case where you have deleted the email account from your device you should stop your iPhone and any other devices from checking for email. The easiest way of doing that is to turn them off.
Once you have done that, change your email password again and check that you can access your email via webmail (on a browser).
If that works you should wait at least an hour and then add the new password to your iPhone and again check it works. If it does then move onto the next device if you have one.
If the above does not resolve the problem, when you change your BT password on an iPhone/iPad/Apple device it may only change for INCOMING mail.
To change the outgoing mail password you have to go into Settings; then scroll down to Passwords & Accounts or on older devices Mail, Contacts, Calendars. From there select the BT email account and select the account where it is listed under IMAP.
You will find the details for the account and can change the password for the Incoming server there, the outgoing mail server only shows SMTP and mail.btinternet.com You have to tap on that Primary Server in order to find where the Outgoing password is hidden so you can update it.
When setting up the email account on your device you are best to set it up manually, using "other" and ensure that you are using the correct settings as per this link.
https://www.bt.com/help/email/manage-email-account/manual-settings/what-are-the-settings-for-outgoin...
