if people don't read or act on the advice given by their e-mail probvider they're hardly like to read and act on anything posted in a third party guide
It isn't just guides this warning should be on, it should also be on the sales page of every ISP
The Advertising Standards Authority has a CAP code on adverts that applies to broadband websites and their phone number checker, broadband availability pages
https://www.asa.org.uk/type/non_broadcast/code_secti...
CAP 3.3 says
Marketing communications must not mislead the consumer by omitting material information. They must not mislead by hiding material information
Material information is information that the consumer needs to make informed decisions in relation to a product
ISPs should be warning people that if they change ISP, they could loose their email account
All well and good but the IPSs are still giving you perfectly good internet access to attempt to log into your Gmail account. It's not the ISP's fault that Google incorrectly identifies access attempts from the new ISP to your existing Gmail account as potentially fraudulent. The ISPs are not doing anything misleading that would require a warning. Their end works.
Feel free to make a complaint to the ASA. I've made quite a few in the past and it's an excellent service but you're going to find that it won't be upheld because the ISP isn't doing anything misleading. You can still access the login page of Gmail - that's where the ISP's responsibility stops.
The problem is with Google's Gmail and the way it determines whether attempts to access an account are likely to be unauthorized. You have to contact Google.
There's a simple answer: If you want reliable email without this sort of problem the proper way to do it is to register your own domain name and pay for hosting. That way,
you are in control - not Google or an ISP. If you're not paying for it, you're not in control. You will also have support available and you can change your ISP and email provider as many times as you like - your email address will stay the same.
At the moment you're using a service which costs nothing and you can now see one of the side effects.