It's 1 in 4 in Kent, 1 in 3 in Trafford.
But Manchester has over 30 secondary schools. How do you suddenly get 10 new grammar schools? Who decides which become grammars? Can they all decide to go selective (no LA control of academies)? How much to build new schools? (Unnecessary free schools all over the place, with secret budgets - try a FoI request to find out how much per-pupil they get...)
So different chance of getting in a grammar school depending on where you live, how many other bright pupils they are in your particular year (you'd pass 11 plus one year, but "fail" the next), and whether you can afford the private tutor (or the prep school).
“At political meetings at the end of the 1960s, Edward Boyle [Minster of Education from 1962 to 1964] was torn limb from limb by conservative voters, infuriated that their children who had ‘failed’ the eleven-plus were being sent to secondary moderns, along with 70-80% of each age group. They had regarded the grammars as ‘their schools’. The eleven-plus, they said, lost them the 1964 election and would lose them every one until it was abolished. Margaret Thatcher recognised this as has every Tory party in practice ever since.” (Simon Jenkins, 2007)