I'm under the impression the UK has half-way decent consumer protection laws, unlike the US. But I'm not sure if it extends to your situation (can't haul it into a physical store for replacement, and not sure if the supplier has any legal obligation to provide a Pre-Paid Shipping label to send in the return).
Here, I usually end up sending the DOA item back at my expense (some exceptions, but it's still paid for - just up-front, as part of an upgraded warranty), wait for them to receive it, then ship out a new one via UPSlow.
The only way to get it faster (assuming there's no upgraded warranty available), is give them a credit card to ship the replacement immediately (essentially purchase the replacement unit). Then they'll do a refund to the CC once they confirm receipt of the DOA unit (funds are slow to return as well). The given excuse is they could get scammed out of a new unit, so this is for their protection. Granted, I can see this to some extent, but not sure what the actual statistics are (how much it would push the retail/street prices up to absorb the losses).
Either way is standard practice here.