Sequencing of newly synthesised RNA can monitor transcriptional dynamics with great sensitivity and high temporal resolution, but is currently restricted to populations of cells. Here, we develop new transcriptome alkylation-dependent single-cell RNA sequencing (NASC-seq), to monitor newly synthesised and pre-existing RNA simultaneously in single cells. We validate the method on pre-labelled RNA, and by demonstrating that more newly synthesised RNA was detected for genes with known high mRNA turnover. Monitoring RNA synthesis during Jurkat T-cell activation with NASC-seq reveals both rapidly up- and down-regulated genes, and that induced genes are almost exclusively detected as newly transcribed. Moreover, the newly synthesised and pre-existing transcriptomes after T-cell activation are distinct, confirming that NASC-seq simultaneously measures gene expression corresponding to two time points in single cells. Altogether, NASC-seq enables precise temporal monitoring of RNA synthesis at single-cell resolution during homoeostasis, perturbation responses and cellular differentiation.