Linker histones are highly abundant chromatin-associated proteins with well-established structural roles in chromatin and as general transcriptional repressors. In addition, it has been long proposed that histone H1 exerts context-specific effects on gene expression. Here, we identify a function of histone H1 in chromatin structure and transcription using a range of genomic approaches. In the absence of histone H1, there is an increase in the transcription of non-coding RNAs, together with reduced levels of m6A modification leading to their accumulation on chromatin and causing replication-transcription conflicts. This strongly suggests that histone H1 prevents non-coding RNA transcription and regulates non-coding transcript turnover on chromatin. Accordingly, altering the m6A RNA methylation pathway rescues the replicative phenotype of H1 loss. This work unveils unexpected regulatory roles of histone H1 on non-coding RNA turnover and m6A deposition, highlighting the intimate relationship between chromatin conformation, RNA metabolism, and DNA replication to maintain genome performance.