Yes, it did allow some kids to get ahead. However, what grammar schools also do is "skim the cream" off and leave the less able children to wallow in what effectively become sink schools. To give you an example, I grew up in a town with 1 grammar school and 2 comprehensives. The grammar school produced kids with grades much higher than the comprehensives, which were basically sink schools.
Of course the Grammar school produced kids with better grades. The motivated/able go into the grammar school, the motivated/able come out of the grammar school.

Put an hard working child into a class of less motivated kids and that child will not inspire hard work in the others. Exactly the opposite will happen, that child might be bullied, and is quite likely to loose motivation.

I disagree with better education being provided on the basis of your parent's income, but in general I agree with better education for those who are motivated. Because of that I feel it's a shame that the Grammar School system has disappeared from large swathes of the country. There are valid debates to be had about whether 11 is too young an age at which to decide which school you go to, and whether there should be more mobility between Comps and Grammars, but at the end of the day I think the principle of grouping students by their motivation (which, perhaps regrettably, is best measured by their success) is a good one.

One thing I am sure of is that the Grammar schools should not have been removed without a ready replacement which provided the same level of education for the able and motivated.