It's a VA/Bur and not a pure Burley, but I'd definitely recommend Solani's Silver Flake (660). I even prefer it to the Aged Burley Flake.
It's been a while since I've tried them and I certainly haven't tested every one, but the C&D Burleys don't really do it for me. There's a characteristic twang to them that I don't care for. But lots of other people love them.
MacBaren's Old Dark Fired has already been mentioned, but the Burley London - Golden Extra - Norwood family is worth exploring too. London is most Burley-centric of them and is unfortunately no longer produced, but you may find some secondhand. (I got a pound recently here on the forums for no more than the original retail.) Golden Extra and Norwood add more VA to the mix, with Golden Extra still being quite close to the Burley London. But I rather like Norwood too and think it's underappreciated. It's a simple tobacco, but pleasant, easy to smoke, and cheap. I've had no problem burning through a couple 100g tins since I first tried it about 6 months ago.