I am having exactly the same issue. I’ve had to move from BT as we can get no TV reception and I’m trying to see my final bill. I’ve had this message about the service being temporarily unavailable for 3 days now.
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I’m seeing the “Service Unavailable. The service is temporarily unavailable. Please try again later” message on Apple’s Safari browser when trying to access MyBT “digitalservices.bt.com”
However, logging in through MS Edge browser MyBT works fine.
I've had that message for at least 10 days in Your Bills / Your Usage and in Your Products I've not been able to adjust voicemail too. The Products do show fine and wi-fi speed test is fine.
Some BT webpages are not displaying when using Firefox or any browser using Mozilla browser engine. The pages only work with Googles "Blink" engine. This means that you can only use Edge, Chrome, Opera etc to load these pages. The known pages affected are Accounts and Billings, Track your Order, Track complaint, Personal Details, there maybe others. It seems to be those pages that contain personnel information that do not load so maybe the Mozilla browsers are more secure.
This situation has now been a problem for 7 days so not sure if BT indeed to fix this with Mozilla browsers, if not this does restrict which browsers can be used by BT customers.
I have managed to get the webpages that do not load to load successfully. Load the main BT webpage in the usual way, go to "account and billings page, you will get the "Unavailable" message. Go to "Tools" at the left hand top of Firefox, select "Page info". In the window select "Security" on next window select "Clear cookies and Site data" A window will open with "bt.com" listed click on "Remove". You should find all O.K. when you look at pages that did not load before.
Could not make things work previously by going to the 3 bar setting menu in the top right hand corner, only worked by clicking on the "Tools" in the top left hand side.
The problem seems quite well commented on in Google's app store at leat 30 comments with the same error message in the past 2 weeks.
I'm using Samsung's in-built browser (Samsung Internet) so the problem with My BT app must be related to the default browser or something. When I use the app on an older phone which just uses Google's Chrome there's no problem.
Still, My BT is forced to close and/or I get that error message. My BT app has worked fine in the past (everything non-browser (https://www) related still works) and it's not had an update for months so I'm assuming it's another problem (obviously My BT is still to blame).
Clearing cookies etc makes no difference on my Samsung Note 10+.