We are rapidly approaching the point where we have sequenced millions of human genomes. There is a pressing need for new data structures to store raw sequencing data and efficient algorithms for population scale analysis. Current reference based data formats do not fully exploit the redundancy in population sequencing nor take advantage of shared genetic variation. In recent years, the Burrows-Wheeler transform (BWT) and FM-index have been widely employed as a full text searchable index for read alignment and de novo assembly. We introduce the concept of a population BWT and use it to store and index the sequencing reads of 2,705 samples from the 1000 Genomes Project. A key feature is that as more genomes are added, identical read sequences are increasingly observed and compression becomes more efficient. We assess the support in the 1000 Genomes read data for every base position of two human reference assembly versions, identifying that 3.2 Mbp with population support was lost in the transition from GRCh37 with 13.7 Mbp added to GRCh38. We show that the vast majority of variant alleles can be uniquely described by overlapping 31-mers and show how rapid and accurate SNP and indel genotyping can be carried out across the genomes in the population BWT. We use the population BWT to carry out non-reference queries to search for the presence of all known viral genomes, and discover human T-lymphotropic virus 1 integrations in six samples in a recognised epidemiological distribution.