I went to a selective grammar in the mid-80s - but as a boarder which required a much higher mark. It was also 13+ not 11+.
Rather than tutoring us, my parents sent us all to a very academic hot-housing prep school that sent a lot of kids to Eton, Win Coll etc every year.
Of the other boarders in my year, over 90% came from preps.
My DH went to a super-selective in his home city and was at a local state primary. He and his brother were tutored for 3 years. Since both got a clean sweep of A's at GCSE and A'Level and both went to Oxbridge it wasn't that they weren't bright enough without the tutoring.
We intend to tutor our DD for entrance exams.
Both for us, and our child, this isn't to try and gain entrance to a school that we weren't/aren't up to the standard of, but because you need to have the extra edge in terms of timing, familiarity to make sure you do well on the day.
Personally I thought the old-style CE was a much fairer way of applying for schools - papers in every subject, with a week of exams. Less chances of someone getting nerves on the one day, better for children who were better than humanities than maths, basically a much more rounded view.