We have accidentally had two AppleTV subscritions for 27 months. How does one go about securing a refund?

You need to cancel one pf the subscriptions and then contact Apple Support for a refund.

click here ➡️ If you want to cancel a subscription from Apple - Apple Support

then here ➡️ Contact Apple Support to request a refund

It is not possible to have several instances of one subscription on one Apple ID account. To have multiple of the same subscription, you would need several Apple ID accounts. Otherwise they’d have to be different subscriptions.

See your subscriptions overview - Apple

Is this about Apple TV+, or a third party channel/​content provider?