OP's question is proper 'length of a piece of string' stuff.
Obviously private tutoring can make a big difference, as can parent-led tutoring, as can good quality private primary education.
A genius [say 150 IQ] kid who's been almost literally raised by wolves, with very poor primary attendance, no books/reading at home and so on, will fail any 11+, always.
And not all 11+ exams are created equal, e.g..
(a) To 'pass' the 'entrance exam' for a non-selective private secondary, if we're talking about a very basic test which is only intended to weed out kids with reasonably serious additional needs, the kid probably only needs to be in about the top 90% academically [i.e. not in the bottom 10%], even the top 95% might be enough... strong primary prep and/or tutoring might well get in even a kid who wasn't quite at that level talent wise in.
(b) To get into a Northern Irish grammar school, which take about 40% of all kids in NI, a kid would in theory need to be in the top 40% for attainment... but in practice many kids don't take the test so it's easier than that... and there are several different way of getting there, e.g. a kid who was in the top 5-10% talent-wise, provided they were entered for the test, would doubtless breeze in even with well below average primary schooling and no tuition... and an upper middle class who barely scraped into about say the top 80% talent wise would very likely make it too, if they'd been to a private prep school and/or been tutored...
(c) Kent grammar schools take in very roughly the top 25% of kids by attainment... but again many kids don't take the test... [you can see where this is going]...
(d) etc
(e) etc.