Laxton Superb is an apple variety that is renowned for biennial bearing, perhaps this is why it never caught on commercially. A shame really because its flavour is excellent.
I try to control mine by thinning but in practice you can only thin if you can reach the fruit easily by hand without Health and Safety issues, so your trees must be low-growing. I understand that research has recently found that for maximum effect thinning should be completed before the largest fruitlets are thicker than the little finger i.e. well before the June drop.
I am trying a lot more thinning this year after a conversation with a expert last autumn at an Apple Day. Most of his (prize-winning) apples, many varieties, are low-growing bushes and most are thinned.