It really surprises me why the UK never caught onto them!!

My husband swears that he did see them a few times, when he was a kid. Says he never saw fresh orange juice until he was around 10+ years old. But yeah, I suppose that squash was just considered easier all around.
But, for OP, I've used the bottled juice concentrates to make exactly what you're making, and it did work out alright. Not
quite the same, but close enough. (That's what the brandy's for.)
I looked for the 'high fruit'/all natural/double-concentrated kinds. Then I just added everything at the same time-- didn't bother pre-freezing the juice. I also don't recall adding much (if any) water, because I tried to compare the concentration strength to that of the frozen stuff, and iirc, it was still slightly less concentrated. And I figured, if it were still a little bit too strong, I'd just add an extra splash of 7-Up when serving.
Since you'll probably want to mix it a few times while it's freezing (to keep it slushy), I'd also recommend freezing it in a large Ziploc bag (if you can find good ones), rather than in a container. In the bag, it's easy to just smoosh out all the clumps. If it's in a container, you've got to take it out and stir, and it can be harder to find/break up any lumps.