@custardcake DD1 was level 5 across the board at the end of Y4. They didn't do (as far as I am aware) the SATs papers when she was in Y3 (at the end of Y4 the advanced kids sat the same SATs as the Y6 kids were doing). She is now at a super selective grammar (which gets pretty much identical exam stats as Tiffins year on year). DD1 was not in any way unusual in terms of maths when she arrived at her current school. I think her English is probably heading towards G&T though. And she wasn't the only one with those sorts of levels at the primary school either. DD2 was level 5 in literacy at the end of Y3 and a level 4a in Maths (she has been taught with older year groups for both of those subjects). DD2 does appear to be way ahead in literacy but there are 3 other kids in her year who are as good or better than her at Maths. DS on the other hand didn't hit level 5 in Maths till Y6 and never hit it in literacy (well, hopefully he is now but we don't get very much feedback from his school, he didn't want to even try for the grammar and is at the comp for which his primary school is a feeder, where he is very happy and settled).
Many primary schools don't push the pupils as much as they could and at that age children develop at different rates anyway, which is obviously one of the arguments against selection at 11+ but it seems clear that there are a core of kids who do hit those levels early on given the opportunity. It doesn't mean the others won't catch up, but schools like Tiffins give those kids the scope to carry on powering forward if that is the way they are going, which is surley a good thing? It seems like Tiffins has more people wanting to go there than they can shake a stick at and I would guess that based on their experiences to date they feel they will fill the places easily even setting the bar high, so why not? If they feel their remit is to provide a tailored education to the sort of kids who are hitting those levels at that age then, given they believe in testing, they need to make the test appropriate. The sad thing isn't that Tiffins sets the bar so high, it's that there are so few state schools that do that or maybe set the bar just a bit lower to capture the kids who are bubbling under (and might overtake the 'hares' in a year or so). So you see the flight to posh schools for those who can afford it - but what happens to those who can't?
One important thing to remember is the kids who end up in super selective schools have often been bullied in their primary schools for being 'swots' or geeky. DD1 was, DD2 isn't, nobody would dare . She's feisty.
Super selective schools are supposed to cater for these sorts of pupils. It's not unreasonable for them to set the test bar accordingly.