The 1944 Education Act (enacted in 1947) was designed for political reasons to solve the problem of an increasing number of workers needed for white collar jobs. Before 1947, most children received only an elementary education (the so-called 3 Rs),but it was becoming increasingly obvious that the need for factory workers was declining. Before 1947, there were only two ways for children to receive an education beyond elementary - most paid for it and a handful had scholarships based on exceptional ability.
The 1944 Education Act enabled a number of current "baby boomers" from poor backgrounds to have a level of education which they wouldn't have had before the Act.Many have been successful (although the booming world economy helped), which is why so many look back to the old days with nostalgia.
However, the world has changed. Manufacturing jobs have disappeared to countries with cheaper labour costs. All pupils have an opportunity for higher level education, so there is no longer a pool of pupils with no chance at all of a higher level of education. Higher education doesn't depend solely on wealth, although we seem to be regressing. The country needs people at all levels to have higher skills.
People seem to forget that comprehensive schools came about, because aspirational middle class parents couldn't get their children into grammar schools. In addition, wealthy parents couldn't buy their way into grammar schools. Unless they were very wealthy their children had to go to secondary moderns, so they preferred comprehensive schools.
Eloethan is right. Children from working class backgrounds who ended up in grammar schools often faced cultural tension between a family which didn't value a liberal education and the aims of the school. To this day, children from professional backgrounds do better than those from working class familes, no matter what the educational achievements or proven IQ of the child is. The former head of Wellington described it as "oiling" ie social skills, networks, etc.