The 1 year free trial came with a subscription to a broadband package.
That package included an Apple TV 4K box, right? That would be the connection. The year offer has always been exclusive to new Apple devices.
I have no Apple subscriptions indicated at all on the ID used
If you redeemed and enjoyed the Apple TV+ offer, then you MUST have that subscription. That’s how that works. Without subscription you wouldn’t have access to Apple TV+.
If you didn’t activate that offer, and never signed up for it, then you wouldn’t have a subscription, nor access to Apple TV+. And then Apple wouldn’t send you reminders.
If you canceled this subscription earlier, then you wouldn’t have this subscription anymore. And Apple wouldn’t send you reminders.
… but an email telling me that the subscription will commence on 30th July unless I cancel it beforehand.
If you have no subscription and never had, then the message is in error, or it is a phishing attempt. With the high level of automation, there isn’t much room for accidental errors.
Identify legitimate emails from the App Store or iTunes Store - Apple Support
Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support
If you are the organizer of an Apple Family Sharing group, then one of the other group members may have activated the offer or subscribed. That might be billed to the organizer after the trial in some circumstances.