There are only two domestic airports with no APD - Jersey and Inverness. You'd need to position there, but no additional avios to connect to London from there.

You still pay the hefty BA YQ though - no UK or EU airports have a YQ restriction like HK does so there's no way to get that low on BA from around here.

Your best bet to minimise cash outlay is to use Cathay Pacific, as they charge minimal YQ. However then you can't use your 241 or upgrade voucher (which I assume is the Lloyds one).