LONDON, Dec 29 (Reuters) - British two-year government bond yields fell to an all-time low of -0.165% on Tuesday, down by 6 basis points since their last trading day on Christmas Eve and edging past a previous low of -0.161% set on Dec. 21. Ten-year gilt yields were 4 basis points lower at 0.22%, their lowest level since Dec. 23. (Reporting by David Milliken, Editing by Paul Sandle)