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Ah, curious. Just did a quick Google on diesel and it tends to come back with lager/cider/blackcurrant which is something that I've always known as a snakebite and black. I've certainly never heard that called diesel in the UK.
As to the coke and lager version - I've never seen anyone order one so difficult to know what it would be called here.
We were having a discussion in the pub the other day about mixed drinks that under-40s would be unaware of:
1) Mickey Mouse - half and half lager and bitter - really a product of the 70s/80s brewing cartels producing so much truly awful keg bitter, the lager killed the taste to some extent. No idea why it was called Mickey Mouse.
2) Brown and mild - a hideously sweet concoction that's kind of redundant now that barely anyone makes mild.
3) Barley wine and lager - used to be a perennial favourite amongst female alcoholics who wanted to reach their destination in a hurry.