By David Milliken

LONDON (Reuters) - Annual growth in British house prices picked up to a three-month high in June in the run-up to the Brexit vote, which has unclear implications for the housing market, mortgage lender Nationwide said Wednesday.

Nationwide said house prices rose 0.2 percent in June - unchanged from the rate in April and May - and that annual growth picked up to 5.1 percent from 4.7 percent, beating economists' expectations of a 4.9 percent rise.

Nationwide economist Robert Gardner said it was too early to judge the impact of Britain's vote to leave the European Union on the housing market, but a lack of homes for sale and high employment rates were likely to keep upward pressure on prices.

Estate agents had a record-low number of homes on their books, partly due to a spike in transactions in early 2016 to avoid a pre-announced increase in purchase taxes for second homes and investment properties which took effect in April.

"It will therefore be difficult to assess how much of the likely fall back in transactions in the quarters ahead is because buyers brought forward purchases ... and how much is due to increased economic uncertainty following the referendum result," Gardner said.

"Gauging the likely impact on house prices will be even more difficult," he added, noting the outlook for London was particularly uncertain due to the larger role played by landlords and foreign buyers than elsewhere in Britain.

Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said he expected the referendum result to push up unemployment and the rates banks charged for mortgages, reducing demand.

"Prices in London ... look particularly vulnerable, given that job insecurity has increased in the City and banks will be thinking twice about high loan-to-income lending," he said.

House prices in Britain as a whole rose 1.0 percent in the three months to June compared with the first quarter, the weakest rate of growth since the three months to September.

Seasonally-adjusted figures showed that prices in London rose 1.4 percent over the period, but were outpaced by rises in Northern Ireland, and areas of southeast England outside the capital. Prices dropped in northern England and Scotland.

(Editing by Toby Chopra)