Well, your situation is more complex than the average player would experience. So, you need to focus on those aspects.
I'll try to explain further.
Normally, players play from the same country they previously registered from. In your case, the UK.
Thus, there is no need to worry about other countries unless you decide to cross borders. Now we're getting to you because you travel a lot, but you are still a UK citizen.
Using your logic, you would need to change your account details each time you visit another country, which is nonsense because, as explained, the registration must meet your citizenship.
Instead, you should consult this situation with the casino to let them know you'll be accessing your account from a different country using a different connection. All those details are monitored by the casino constantly, and each change may result in additional security checks. Thus, it is always better to consult your plans before you leave the country.
The casino support will explain whether you can or can't play from other countries. Always consult with chat or support. This is very likely stated in the terms and conditions.
Please note that not every restricted country is always blocked; the best option is to
a) ask the support
b) consult terms and conditions
c) check the registration form
The casino does not verify incoming deposits; they verify you once you win and ask for the first withdrawal. Making a deposit is solely your choice, so it is important to always register with a full and correct address.
If you can't find the land in the registration form and pick something random, no one will notice unless you undergo the KYC.
Is it better now?
I suggest you check out this free e-course called "iGaming Player Verification and AML" which might help you understand the logic behind the process.