In England, there is currently heightened political interest in increasing mathematics attainment and maximizing post-16 participation. The latter is not merely an issue for upper secondary but requires a long-view of students' mathematical progress. This paper reports such a system-level overview of the mathematics education pipeline in England based on analysis of linked data from the National Pupil Database (NPD) and Higher Education Statistics Agency (HESA). A sequence of mixed-effect logistic regression models at each phase of the education pipeline are developed to predict attainment in General Certificate of Secondary Education (GCSE), A level and undergraduate mathematics and participation in post-16 and university mathematics. In particular, we focus on the impact of prior attainment and student demographics: gender, ethnicity and socio-economic status. The analysis identifies four important findings. Firstly, female participation and attainment in A level Mathematics and Further Mathematics is lower than that of male students, which impacts their representation in undergraduate mathematics, despite them marginally outperforming male students at both GCSE and degree level. Secondly, the attainment and participation of students of Asian ethnicity in GCSE and A level Mathematics is striking in its positive divergence from the trends of other ethnic groups, whereas White students have higher attainment than other ethnic groups at university. Thirdly, many students from poorer backgrounds fall behind their peers during years 7 to 11, and their participation and attainment in A level Mathematics is also reduced compared to their more affluent peers. Lastly, students who study A level Further Mathematics are more likely to study undergraduate mathematics, but they are no more likely to achieve a first-class degree, compared to those who haven't studied Further Mathematics. The findings should be informative to policymakers and other stakeholders who can put in place enhancements and interventions to improve the outcomes for underrepresented groups.