I don't know who marked @EA_Darko his reply as a "solution" but it is not.
Finally found a workaround for what I consider to be a bug. AFAIK it can occur on the PS4 and the Xbox One.
1. What is the problem?
You start an EA game (like Star Wars Battlefront) and you get an error message saying that you need to input a security code to access your EA account. This code was supposedly sent to (one of) your e-mail address(es) associated with your EA account.
This code is not sent nor will it be re-sent if you choose so. You can also opt to send the code to another e-mail address. The code will not be sent there either.
You can fill in as many mail addresses as you want but only the last one is remembered. You cannot let the code be sent to your first mail address once a second one is used. This is because when you fill in the first one again you'll get the error "Duplicate e-mail address".
Note: your Origin- and EA accounts are one and the same account concerning this.
2. What does not help
On-line chat with the Help Desk. They will eventually say that there is a technical problem that they are working on.
Adding a secondary e-mail address to your EA account via the 'Security' tab. Nor does activating 'Login verification' with an SMS via the 'Security' tab.
3. What causes this problem?
I wish I knew.
4. The workaround
In the window that pops up to ask you for the code that was never sent you can choose to let it be sent to another e-mail address. Fill in a completely bogus mail address there (i.e. like a cat walked on your keyboard). Just to be sure let it end in "@gmail.com" or something like that.
An e-mail will be sent to one of your "real" e-mail addresses that EA knows off. In this e-mail they'll ask if its all right to make this change. Click on the link in that mail to say that this is NOT okay.
For some strange reason you will be logged in without EA asking you for a security code.
5. Other notes
Took me 3 weeks to find this out. Bloody EA!
Never change e-mail addresses. EA remembers ALL OF THEM, even though you deleted them from the main account.
According to EA it is possible to connect your Microsoft account (needed for on-line Xbox play etc.) to your EA account. For this you must go to help.ea.com (NOT ea.com!) and choose to login to your account. Then, do NOT log in w/ your email address and password, just leave these fields empty. Instead, click on the icon with the text "Xbox Live". This wouldn't work when I had the security code problem. Now it does work though.
For some games, like Battlefront 2, even single player REQUIRES an EA account. For loot boxes and cards etc. Without these you can NOT progress or play the game properly. Your progress is not saved locally and synchronized with "the cloud" (i.e. your EA account), instead it is ONLY saved in the cloud.
EA really, really needs to review their on-line login procedures because they appear to be seriously broken.
EA needs to be clear and honest about problems to employees, to customers, on their website and on their forums.