You have to try ebuyer (http://ebuyer.com) shipping. It blows my mind when I order from them how fast they can ship, I've ordered at ~10:45PM (11PM cut off) and had it ~7AM the next day, I still can't comprehend how well oiled their shipping process must be to get that done.
They are based not far from Leeds, and a friend of a friend worked there. So while at Uni I used to be able to ring up about 4pm and get it "delivered" at about 6 :)
But, yeh, they were also pretty impressive for me outside of that.
Computer components is a niche that Amazon aren't quite king of yet (sorta).
I opted for 1day once when I needed a new monitor ASAP. When you're already paying $250, $4 for one day shipping seems cheap. Two day shipping occasionally gets here in one day, but sadly I'm late in the UPS delivery route so nothing shows up until 4pm in the afternoon...
I've had Prime (US) for awhile and I couldn't be happier with it. I don't think I've ever opted for 1-day shipping, but I'll often receive items next-day anyways.
It's pretty rare that I opt for the 1-day, but when I do, it's awesome. The other day, I ordered something at 3pm and got it 9:30am the next day.