Other than setting up your own vpn server back to a BT Consumer broadband connection afraid not.
Ip address are assigned by providers or carriers.
Unfortunately the error you are seeing is because you're trying to access the BT account and probably multiple times from a non UK registered IP address which has therefore meant you will be redirected to that TS-0003 error page.
You would need to login from an IP address within the UK to access the BT account from the browser.
As you have seen SMTP and IMAP connection should be ok.
I know what the T&Cs state, I posted them in my message and no where does it state what you have stated in your post.
I asked you "Can you point out where BT state in their T&Cs that the email system needs to be accessed from the UK and can not be accessed using an IP address out side the UK and they will prevent BT customers from accessing their email unless they are using a known VPN? because that is what you stated in your post when this is blatantly not the case when thousands of people who holiday in Spain and other people have property and live there for up to 90 days at a time have no issues what so ever accessing the BT email accounts either by webmail or email clients and include myself in that.
As already stated, I'm going by the error code and aligning that to the terms as to why that error is appearing.
Error code TS-0003 when logging into the BT Consumer Siteminder SSO gets invoked when you are either trying to login to the BT account from a known VPN or from an IP address not registered within the UK.
You maybe able to login a few times from a non UK IP Address before that measure gets invoked, but once invoked you are redirected to the TS-0003 error code. To get around that error you need to use an IP address that's registered in the UK.
It may also be tied up, as it used the same BT Siteminder, to protect other parts of BT Consumer services such as BT Sport.
It may be what the error code is stating, although I doubt the error code is accurately reflecting what the error is and in event what you have stated it is not in the BT T&Cs.
I also doubt that "You maybe able to login a few times from a non UK IP Address before that measure gets invoked, but once invoked you are redirected to the TS-0003 error code. To get around that error you need to use an IP address that's registered in the UK" because I and other BTMail user that I know log access their BT email account more than "a few times" when in Spain and other countries without any problems what so ever and are you honestly suggesting that BT will not allow their customers to use their email account while on holiday!
You can let us know when you go over. It does however seem like there's been a change as the percentage of reports involving the invocation this error code seems to have increased or BT's updated their IP address geolocation database and blocklist with more IP addresses.
As I said, I would find it bizarre and totally unacceptable and no doubt other customers would as well, if BT are blocking your personal email account and preventing its use while outside the UK on holiday or an extended stay.
I am going to Spain in a few weeks time so will update.
As an update to the above:
I have been in Spain for a number of days now and I have had no issues sending and receiving numerous emails using an email client using IMAP on both an Android phone and Android tablet. I have also tested using webmail and there were no problems.
This has been the case while using wifi and 4g.
I think problem when use a lot the webmail, my uncle never use a client such as thunderbird.
I tested with both webmail and an email client.
I have no doubt that BT are not preventing their email being used out side the UK and to suggest they are is nonsense.