I am happy to report that the replacement programme for problematic Apple TVs is still in effect.
I returned my faulty Apple TV today (error code -3906) to Stormfront, an Apple Premium Reseller in the UK, and they confirmed that it was eligible for replacement.
My Apple TV's serial number ended with DRHN and had the relevant alphanumerics in the fourth and fifth positions, not the third and fourth, as stated above.
As per previous posts, the unit could not be swapped in-store; I will have to return to collect the replacement when it arrives.
Staff were excellent and very helpful. Things they asked:
They then tested the device's ability to connect to wifi in-store; it failed with error code -3906.
Hope this helps someone else!