I've given up , I think. I have two gmail/google accounts. One is loaded, has been loaded for a long time and has no issues. The second gmail account was loaded for a long time also, the account is almost as old as the first, like 10-12 years or longer. I-phone 7, up to date, let me look again...yep, software version 15.5, I updated to this in the last few weeks.
The problem is with the second gmail account. It disappeared. I've tried re-adding it and there is nothing magical about doing so. I open the mail app and select the option to add an account. I've tried too many times to recall. The result is a continued message cookies are disabled in my browser. I've enabled cookies on Safari and I also use Firefox enabling cookies on both with no success. I've uninstalled Firefox and made Safari the default browser, enabled cookies, reinstalled Firefox , made it the default browser again, assured cookies are enabled on Safari although not the default browser...I give up. I'll just have to use the second gmail account on my laptop. Incidentally, I even thought maybe something weird with the only browser I use on my laptop (connected to internet via wi-fi with Verizon service provider) so enabled cookies there , went through the process again and again trying to add the second gmail account on my I-phone 7 with same resulting message, " Your browser has cookies disabled. Make sure your cookies are enabled and try again."
I guess I can try contacting google. While there is nothing perfect in this world, this is none the less bizarre as I've used both gmail accounts on I-phone for at least five years I can recall. I've even more recently in the past year set up an account with aol and added it via I-phone mail app with no issue.
I've tried everything that has been suggested in this forum. No big deal, I'll live, it's just that for so long my primary e-mail account with gmail, google, is the one I use more often and cannot add it to my I-phone, it simply disppeared. Iv'e tried google's mail app but should be able to add the account via the Apple mail app. No luck with the google app either. Like I said, maybe try contacting google. The e-mail account in question works perfectly on my wi-fi connected laptop. So I'm just disappointed I cannot determine a fix. :-)