At my secondary school it wasn't possible to do more than 6 GCSEs vs. many of the most academically gifted independent school attendees who obtained at least double that number of GCSEs.

At A level my secondary school couldn't accommodate most A level subjects: students were sent off to many different schools for different subjects, and forced to choose which A levels they did based on complicated scheduling arrangements. The only reason some of them could afford to do A levels was because of the £30 benefits payments they received which covered their transport costs (I believe it was called EMA (something like "Education Maintenance Allowance") at the time, but it was a long time ago).

As far as I recall, the maximum possible qualifications from my secondary school was 6 A* GCSEs and 3 A levels.