Welcome to Android Central! Open the Email app, tap Menu>Settings, select that email account, and look for a Remove Account option. You might have to tap the Menu button again to see the option.
OK that is sort of right and it put me on the path of solving my problem and realizing my mistake, so many thanks for you help.
This was the scenario, and my initial mistake.
GMAIL is the only EMAIL APP that I have on my phone.
I already had 3 standard Gmail Accounts - they are no problem and I want to keep them
I added a personal(POP3) account to my phone using:
GMAIL/Settings/Add Account/(Set up Email). This is the account I wanted to remove.
So the answer is:
Go into the GMAIL app.
Right swipe to bring up your list of email accounts:
select Manage Accounts, which for me listed the following:
Google (Email Accounts, I have 3)
Personal(POP3) (Accounts I have 1)
+ Add account (option)
I selected POP3 accounts, and this lists my POP3 Account name, but because there was only 1 account, I hadn't bothered to select it, I assumed the menu option would show all options, because it was the only account (My MISTAKE), the menu option only shows the "sync" option.
Because I had multiple Google Gmail accounts, I had naturally always selected one before tapping the Menu Options, so they always included the Remove account option.
So even though there was only one account you still need to select it and when you do, and then tap the Menu option, it now includes the Remove Account Option.
Problem solved.