The Telegraph is listing Tim Peake to be the 8th Briton in space. However, 2 of the 7 before him on their list are actually Americans who happened to be born in the UK (Greg Johnson and Richard Garriott). Michael Foale, Piers Sellers and Nicholas Patrick all flew for NASA as US citizens, although they appear to hold dual nationality. Michael Shuttleworth (dual UK/South African) paid for his own trip as space tourist. Arguably, Helen Sharman is in a similar category as she was funded by industry for a one-off project, essentially for the sole purpose of putting the first Briton in space.
Tim Peake is a 100% British astronaut flying on behalf of a space agency as a full crew member on a science mission.
Good luck Tim!