LONDON, June 29 (Reuters) - British house prices rose by 13.4% in June compared with the same month last year, the biggest annual increase since November 2004, mortgage lender Nationwide said on Tuesday. In monthly terms, house prices were 0.7% higher than in May, Nationwide said. Economists polled by Reuters had expected prices to rise by 13.7% in annual terms and by 0.7% from May. (Writing by William Schomberg; editing by James Davey) Our Standards: The Thomson Reuters Trust Principles.