The pandemic forced many education providers to pivot rapidly their models of education to increased online provision, raising concerns that this may accentuate effects of digital poverty on education. Digital footprints created by learning analytics systems contain a wealth of information about student engagement. Combining these data with student demographics can provide significant insights into the behaviours of different groups. Here we present a comparison of students' data from disadvantaged versus non-disadvantaged backgrounds on four different engagement measures. Our results showed some indications of effects of disadvantage on student engagement in a UK university, but with differential effects for asynchronously versus synchronously delivered digital material. Pre-pandemic, students from disadvantaged backgrounds attended more live teaching, watched more pre-recorded lectures, and checked out more library books than students from non-disadvantaged backgrounds. Peri-pandemic, where teaching was almost entirely online, these differences either disappeared (attendance and library book checkouts), or even reversed such that disadvantaged students viewed significantly fewer pre-recorded lectures. These findings have important implications for future research on student engagement and for institutions wishing to provide equitable opportunities to their students, both peri- and post-pandemic.