Seems he's relying on a common law definition of cheque, but not one that will clear the cheque clearing systems. Arguably IF BT presents the cheque for payment, to their bank, the cheque won't clear, and therefore will bounce.
Under the common law though, they can present it to his bank, or to him specifically for payment, and it probably could be honoured.
They're probably ultimately right, but it's not worth anyone's time to enforce it. Well, maybe it is to the lawyer.
He'd probably be seeking a declaration from the court that it was valid satiation of the debt. Basically the court saying to BT, you've been validly paid, now go away.
Really creative and entertaining though, and I hope BT backs off because their "Bill payment" fee is probably deserving of some kind of a consumer protection law smack upside the head.