There is significant amounts of Neanderthal genes in British (and all European ) genomes.

"Neanderthal-derived DNA was found in the genome of all contemporary populations". [1]

[1] https://en.wikipedia.org/wiki/Interbreeding_between_archaic_...

See also: https://www.sciencemag.org/news/2019/01/genetic-data-half-mi... ( Genetic data on half a million Brits reveal ongoing evolution and Neanderthal legacy )

https://science.sciencemag.org/content/358/6363/655 : "We find that non-African populations outside Oceania carry between 1.8 and 2.6% Neandertal DNA"