The 11+ and grammar schools did work for a few years, because they provided a few places for children, whose parents would never have been able to afford a grammar school education. However, there was a lack of consistency. Some areas had more places than others, so it was never fair. More importantly, the 1944 Education was formulated in the context of a pre-war society. A minority went on to have white collar jobs and it was only considered necessary to provide those few with a proper secondary education. The majority of people worked in manual jobs and academic learning wasn't considered relevant. With hindsight, this was a huge mistake, because countries such as Germany were providing quality vocational training and apprenticeships.
After WW2, there was a huge increase in white collar jobs and even manual work became more technical. Socially aspirational parents wanted their children to work towards less 'dirty' jobs and it was realised that secondary moderns just weren't providing the opportunities (although some secondary moderns were better then others). During the 1950s, some of the most vocal supporters of comprehensive education were in the shire counties, such as Leicestershire, because there weren't enough grammar school places for the children of the upwardly mobile parents.
Fast forward to the current day...our economy needs more skilled workers at every level. Anna Vignoles, a professor of education at Cambridge who has done a huge amount of research on social mobility and education, says that we have enough 'highly educated' people to do the top jobs. She claims that what the country needs to do is concentrate on those in the middle of the ability range and upskill them for the demands of the modern world. The return of grammar schools won't do that.
I'm at a loss to understand why Theresa May thinks grammar schools are a good idea.
PS. My own children were the first in my family to go to comprehensive schools. I was a little nervous at first, but I honestly think they had a better education than I or my parents had. Both have gone to good universities. My daughter found a good job after graduating and is more well-balanced than I was at her age. My son is just starting his degree and I'm reasonably confident he'll be OK. They're both bright, but I don't think they have suffered in any way from not going to grammar schools.