It's the nature of some 11+ exams that separates the 'Alicias from the Aleeshas',(!) not (arguably) the exam itself. The grammar schools as instituted under the 1944 education Act would surely have promoted social mobility, in that every child attending a state school, whatever their background, had access to the exam, and success in it provided a free academic education, that had previously been the sole preserve of the rich and privileged.
When I took it in the (late!) sixties, tutoring for the exam just didn't happen. There was no need. The primary schools themselves provided the practice. You didn't have to apply to take it, you just did. And in my day the 11+ was more of a raw I.Q. test, rather than an exam depending upon curriculum based knowledge, which many are now, and which will obviously favour children whose parents can afford tuition or private education.
It really was more of a net, in those days, to stop the brightest state school children from being denied an education suited to their ability, just because they were poor. Poor children did go to grammar school, if their parents wanted that for them.
As usual, the middle classes have latched on to something originally intended to help iron out wealth-based disparity, and run with it. (That includes me btw
). That's what happened with the Public Schools, some of which were originally established as charity schools for poor scholars!
I'm against selection in theory (would much rather see an excellent local comprehensive that every child could attend - life would be so much more angst-free!), but I'm ambivalent about grammar schools in RL, as in some areas they seem to be the only option if you want a decent education for your child, and two of my dc have attended one. Where they have been retained, however, I do feel very strongly that the exam should be accessible to all, and it definitely isn't, not where I live, anyway.