I have used GiffGaff successfully in 2019 too, but I have just been in the USA and tried to use a different SIM - Asda Mobile PAYG, piggybacks off Vodafone. My phone is dual SIM. I got a phone signal but no data, although I didn't actually try making a call to see if it worked. There was just no internet connection. Switching back to GiffGaff was OK, but the Asda Mobile still didn't have data when switching back. Checked all account settings etc and that international data roaming was on, and re-downloaded the "settings" for the provider and rebooted phone. Several times.
I sent a message to their customer support while I was there but didn't get a response. Since coming back home, I've had a text, not sure if it's a response to my message if or if they just sent it anyway:
"Hi, we'd like to make sure your phone can access data abroad if you're planning to travel this summer. We've previously sent settings to your phone which should already be installed. Sometimes these settings may have been missed - please visit
http://mobile.asda.com/APN for info on how to check if you have the correct settings before you travel. We'll also be resending settings to you in the next few weeks. Please follow the instructions when you receive them."
I think my situation might be complicated with the phone being dual SIM. It does indeed store the settings separately for each SIM but I have to assume it switches settings correctly when you switch SIM. But anyhow I checked that page that they referred me to and the APN name was different. I had "Vodafone UK Data" wap.vodafone.co.uk and the web site says it should be "ASDA Internet" MY.INTERNET.
I've now changed that, so I'll see what happens next time and whether it changes again when they eventually proactively send me the settings. (And why I didn't get the correct APN when I used the Download Settings on the phone before, I don't know).
This is not the same situation as yours, but just letting you know the type of thing that can go wrong. Obviously, contact EE to see if they have a solution (maybe as others have suggested your phone is locked to EE - but I would have thought they'd have a solution for roaming in that case - the APN should allow a partner provider to connect when abroad, although I don't knwo the technical details as to how this would work), but is there a page like Asda where they provide what the settings should be so you can check that in your phone?
[EDIT:
https://community.ee.co.uk/t5/Mobile-Data/EE-APN-Settings-Where-to-find-them/td-p/1145404
iPhone
You are unable to update/change APN settings on an iPhone as these are locked out by the network. These are done by Carrier updates."
Buit the APN appears to be "everywhere" for Android. ]