Hi! I Had the exact same problem as you did. What helped me was a combined fix of all the above.
1) Put your iPhone/iPad in airplane mode
2) Fully switch-off your phone
3) Turn it back on
4) When prompted enter your access code, but don't unlock your SIM
5) Your iPhone/iPad is booted
6) Go to your mail app
7) Go to Outbox
8) You should be able to click on edit in the top-right corner
9) Click on the circle in front of your e-mail
10) Delete
You can reactivate cellular and wifi data at this point, turning off airplane mode should prompt you to enter your sim.
Good luck!