I live in Britain so I don't really have a list of specifically "British" names, because they're just names! (I do have names which I consider distinctly American though!)
These are some names which are reasonably popular in the
UK but unusual in the US, so I suppose they could be considered British names...
MaisieFreyaFlorenceLolaEsmeIslaTillyMillieRuby
ArchieAlfieHarveyCharlieCallumOscarTobyArthurFinlay