I was asked this question by a fellow iPhone user. Although I have set up Gmail on my iPhone, I hardly use it but just now, I checked it to see if there really is no way to sign out iPhone email. True enough, there is no option to do so and I think this is rather risky if we do not lock our iPhone with a password, like myself.
To work around this, if we do not want to use email anymore, just go to SETTINGS –> Mail –> Accounts [Gmail or whatever your account is] –> Account –> and turn it OFF.
Once it is OFF, when you access your email via the Mail icon on your SpringBoard, you will see this on your screen.
Of course, if you would like to take extra precaution, after turning your email account OFF, delete the password from the Incoming Mail Server and Outgoing Mail Server (SMTP) of your IMAP Account Information.
Remember to add in your password and turn it ON again when you want to use it. Yea, I know it’s a little tedious but then what to do when there is no direct option to keep the email logged in or out.
If you know of a better way, do share by leaving a comment. Thanks.