School closures due to COVID-19 have been predicted to have a large impact on pupils' learning and wellbeing. Systematic evidence about teachers' perceptions of what challenges their pupils have faced, and how they have been addressing these challenges, will be important for post-pandemic planning. We interviewed 24 teachers from English state mainstream primary and secondary schools in June 2020 and asked them to describe the impact of partial school closures on their pupils' learning and wellbeing, and how they had been addressing challenges as individual teachers and at the whole school level. Data were analysed using reflexive thematic analysis. Six themes were identified: (a) "pedagogy and process," (b) "communication with pupils and families," (c) "life at home," (d) "the role of parents," (e) "a COVID-19 curriculum," and (f) "moving forwards and making plans." Teachers reported difficulties in navigating the new form of education and finding the most effective way to teach and engage with the pupils. Pupils' lack of routine and their home environment were seen as influencing their learning and wellbeing. Parents' differing levels of involvement raised concerns about inequality. We discuss the practical implications of how to support pupils' learning and wellbeing both during and after COVID-19.