Not a brit nor a lawyer. But I thought it was simply called the "High Court of England and Wales" and that the judgments were binding throughout the UK.
Nope. The UK is funny. Unlike several 'federated' countries in which each 'bit' has equal power over it's area as each other, the UK has a mismatch. England and Wales are treated together as one country lots of things (law, health system, same notes), but Scotland has a separate legal system, Northern Ireland would have separate laws aswell, but that's a special case cause it has a ahem unique parliamently system.
Wait till you look at other oddities, like the Isle of Mann, which isn't in the UK, or one of the channel islands, which only abolished their feudal voting system a few years ago.
It is called the High court of England and Wales because Scotland has a different judicial system. I doubt any Scottish judge would not consider it as highly persuasive however.