The Department publishes the number of pupils at the end of key stage 4, who are eligible for free school meals (FSM), in its characteristics statistical release, available to view here: https://www.gov.uk/government/collections/statistics-gcses-key-stage-4.
The Department published the number of A level students, at the end of their 16-18 study in 2016/17, who were eligible for FSM, in its statistical release.,  The number of A level students at the end of their 16-18 study, who were eligible for free school meals from 2011/12 – 2015/16 are:
Number of A level students eligible for free school meals
 For 2014/15 – 2016/17 select the ‘revised’ publication from the top of the page, open the ‘characteristics national tables’ then select tab ‘table CH1’. The ‘number of eligible pupils’ column for the ‘FSM’ row provides the required figure. For 2011/12 – 2013/14 select the relevant ‘attainment by pupil characteristics’ link (half way down the page) and open the ‘national and local authority tables’, open tab ‘table 1’ and take the ‘number of eligible pupils’ from the ‘FSM’ row.
 FSM status in 16-18 study is based on the students eligibility in their final year of key stage 4 study. The methodology through which student’s FSM eligibility is identified was changed in 2016/17. Up to 2015/16 a student’s FSM was taken from their census record three years prior to the academic year the figures are reported for. In 2016/17 a student’s FSM is taken from the census record of their final year of key stage 4 study (normally, three years prior). Due to this change, 2016/17 figures can not be compared to earlier years. FSM eligibility in key stage 4 is taken from the census record for that academic year.
 https://www.gov.uk/government/statistics/a-level-and-other-16-to-18-results-2016-to-2017-revised - open the ‘A level exam results and A level and vocational participation csv’ link, open the ‘performance measures by characteristics’ file and then filter column E for ‘FSM eligibility’, column F for ‘eligible for FSM’, column G for ‘A level’ and then use the figure for ‘number of students’.
 Figures based on final data. Figures for 2015/16 and 2016/17 are based on revised data.
 Figures from 2012/13 to 2014/15 cover students at the end of advanced level study who were entered for at least one A level, applied single award A level, applied double award A level or combined A/AS level in the reporting year. Figures for earlier years cover students who were entered for at least one A level, applied single award A level, applied double award A level or combined A/AS level in the summer of the reporting year.
 Figures for 2015/16 onwards cover students at the of advanced level study who were entered for at least one A/AS level, applied single A/AS level, applied double A/AS level or combined A/AS level during their 16-18 study. As a result there has been a large increase in the number of A level students since 2016 and therefore figures are not directly comparable to earlier years.
 In 2015/16 the figures are only based on students included in the ‘best 3 A levels’ measure. In all other years, all students are included.