Several minutes of unskippable ads on app startup

The Apple TV app’s main screen (Home) would show what it has to offer as (for me) 19 or 20 background images (at 8 sec. per image) for various content, but you can navigate up (or ↰ Back) to get the side menu with tabs, or navigate down to browse the content overview for the current tab — at any time. Nothing to wait for.

There are no other ads in the Apple TV app, than for content that is available through this app.

Additionally, the start of an Apple TV+ episode may begin with a skippable recap or sometimes a skippable mention of a different Apple TV+ show, although I haven’t seen the latter happen in a few weeks.

Apple TV app user guide for smart TVs and third party streaming devices - Apple Support

If you experience something different than I do on my Samsung TV, then please contact the Apple Support staff for their guidance.

Are the ads you are seeing for Apple TV shows? If not, those ad are not coming from the Apple TV app and are coming from another source in your setup. The Apple TV trailers also display a "Skip" button on the screen, so if you do not see that when the trailer/ad starts, then that also confirms it is not coming from your Apple TV app.

Possibly you or any person with the remote had accidentally pressed Select (often the middle button in between the directional buttons), to access a trailer for the then-presented movie or show? Just a guess.

Remotes with a Back button or Menu button should always be available to back out of anything that is playing in any app. Possibly it requires multiple pressings of this button.

The Play/Pause button should also be able to halt playback.

I don’t have access to the Apple TV app on a Virgin Media box, but I can’t imagine that it would be radically different to how Apple’s app behaves on other platforms, like newish smart TVs or other TV-connected streaming devices.

If this behavior returns, then please give feedback to Apple, as guidance on how to improve their app with future versions. Thanks.