LONDON, July 20 (Reuters) - Britain's jobless rate fell in May to its lowest level since 2005 as the labor market strengthened in the run-up to last month's vote to leave the European Union, official data showed on Wednesday.

The unemployment rate fell to 4.9 percent in the three months to May, the lowest level since the three months to October 2005 and down from 5.0 percent in April, the Office for National Statistics said.

Economists polled by Reuters had expected it to remain at 5.0 percent.

Bank of England policymakers will be watching closely how Britain's labor market reacts to the vote to leave the European Union, having warned slower growth and higher inflation are likely to result.

Wages continued to increase ahead of the referendum as expected, with pay including bonuses rising 2.3 percent in the three months to May - the biggest increase since October 2015.

The recent increase in wages in part reflects the introduction in April of a new, compulsory National Living Wage of 7.20 pounds an hour for workers aged 25 and above, a 50 pence rise on the existing minimum wage.

Before the June 23 referendum, the International Monetary Fund and Britain's National Institute of Social Economic Research said wages, rather than jobs, were likely to take the strain of the adjustment from a vote to leave the EU.

The claimant count rose by 400 people in June following a rise of 12,200 in May, a sharp upward revision. June marked the fourth consecutive rise in the claimant count, the first such run since the months leading up to September 2011.

The number of unemployed fell in the three months to May to 1.646 million, while the number of people in work rose by 176,000 to 31.705 million - taking the employment rate to 74.4 percent.

A survey from the Recruitment and Employment Confederation showed the number of permanent staff hired via 

recruitment firms fell for the first time since December 2012 - around the last time Britain's economy flirted with recession.

Another survey of chief financial officers from Deloitte, conducted after the referendum, showed fewer than 1 percent planned to increase hiring in the next year.

(Reporting by Andy Bruce and Ana Nicolaci da Costa)