It was even more difficult in Barnsley to move from sec. mod to grammar school because we had an extra layer of 'central' schools which were 'technical' and effectively halfway between. Kids going there might expect to end up with a job as a plumber or electrician or typist or nurse (in the days when you could become a nurse with only 2 O levels). The central school kids were clever but probably not academic. They would be expected to try for O Levels - but if any wanted to stay on to sixth form to do A Levels they had to go to one of the three grammar schools. We had about half a dozen Central school kids move into our sixth form year, but that's the first transfer I can remember. If anyone moved up from a sec. mod. at 13 it would likely be to a central school, not all the way up to a grammar school.