According to wiktionary, the British pronunciation is /ˈpɹɪv.ə.si/ and American pronunciation is /ˈpɹaɪ.və.si/.
Recently I watched a British show, one of the people on the show, who is from England, used the later pronunciation. Are both pronunciations used in British English.
(In case someone is curious, the show was 10 O'Clock Live, in the discussion about Edward Snowden, Jimmy Carr was consistently using the pronunciation ˈpɹaɪ.və.si and David Mitchell pronounced it as ˈpɹɪv.ə.si.)