Moreover there should be still one popular blend in the UK of which existence most people seem to have forget, namely, Mc Barens Original Flake formerly known as Walnut Flake by Ogdens of Liverpool
Mate, we get about 20% of the choice you do in America. Cornell and Diehl alone probably produce more different blends than everything put together in the whole of England.
Decades ago, when it was available in the states I tried JF Germain's Brown Flake. It was described as virginia leaf but it seemed like it was an air-cured variety and therefore smoked more akin to a very mild straight burley. Assuming it hasn't changed much this might suffice.
I've heard of a burley flake called Singleton made by STG but I don't know if it's available in the UK and I've never seen it in the states.
I tried looking but there doesn't seem like much Peter Stokkebye is available from UK tobacconists. If you can find it their Dutch Cavendish is a burley forward blend with a slight smoky note. Also, they have Burely 702 but I can't recall exactly what it is like other than a straight forward non-aromatic tobacco.
I have a couple of packs of Original in the queue, untried, occasionally fill up with Revor and enjoy the earthy flavour of Germain's Brown Flake (a VA) but quite impressed by the wheaty, biscuity Solani Aged Burley 656 currently in my rotation.
There are quite a few VaBurs, from Gold Block to University Flake to Ennerdale - burley carries flavourings best of all, it seems.