UK house prices fall for 3 months in a row, first time since 2009 -Nationwide

* House prices drop for 3 months for first time since 2009

* Nationwide reports weakest annual house price growth since 2013

* Figures add to signs of household slowdown (Adds graphics, reaction and detail)

By Andy Bruce

LONDON, June 1 (Reuters) - British house prices fell for a third consecutive month in May for the first time since 2009, according to a survey on Thursday that underlines the housing market's slowdown since last year's Brexit vote.

House prices fell 0.2 percent month-on-month in May, compared with a 0.4 percent drop in April, mortgage lender Nationwide said. A Reuters poll of economists pointed to a drop of 0.1 percent.

Year-on-year, house prices were 2.1 percent higher, marking the weakest annual growth since June 2013 and slowing sharply from growth of 2.6 percent in April.

With Britons just over a week away from voting in a national election, the figures added to signs that they are reining back spending in the face of higher inflation fuelled by rising energy costs and the weakened pound since the vote for Brexit.

Bank of England figures on Wednesday showed the number of mortgages approved by lenders slid to a seven-month low in April.

"It is still early days, but (the Nationwide survey) provides further evidence that the housing market is losing momentum," said Robert Gardner, Nationwide chief economist.

"Moreover, this may be indicative of a wider slowdown in the household sector, though data continues to send mixed signals in this regard."

Investec (LSE: INVP.L - news) economist Victoria Clarke said the Nationwide figures were consistent with fading household spending power, with retail sales also weakening this year in spite of robust consumer confidence.

"Our suspicion is that the housing market will continue to remain subdued," Clarke (Toronto: CKI.TO - news) said.

Rival mortgage lender Halifax said British house price growth was stuck at its weakest level for nearly four years in April.

Other parts of Britain's economy appear to be faring better.

British manufacturing chalked up its second-fastest growth in nearly three years last month, putting the sector on track to shrug off election and Brexit-related uncertainty and improve on a weak first-quarter performance, a survey showed on Thursday.

(Editing by Catherine Evans)