Hybridisation may lead to introgression of genes among species. Introgression may be bidirectional or unidirectional, depending on factors such as the demography of the hybridising species, or the nature of reproductive barriers between them. Previous microsatellite studies suggested bidirectional introgression between diploid Betula nana (dwarf birch) and tetraploid B. pubescens (downy birch) and also between B. pubescens and diploid B. pendula (silver birch) in Britain. Here we analyse introgression among these species using 51,237 variants in restriction-site associated (RAD) markers in 194 individuals, called with allele dosages in the tetraploids. In contrast to the microsatellite study, we found unidirectional introgression into B. pubescens from both of the diploid species. This pattern fits better with the expected nature of the reproductive barrier between diploids and tetraploids. As in the microsatellite study, introgression into B. pubescens showed clear clines with increasing introgression from B. nana in the north and from B. pendula in the south. Unlike B. pendula alleles, introgression of B. nana alleles was found far from the current area of sympatry or allopatry between B. nana and B. pubescens. This pattern fits a shifting zone of hybridisation due to Holocene reduction in the range of B. nana, and expansion in the range of B. pubescens. This article is protected by copyright. All rights reserved.