By Ann Saphir

June 30 (Reuters) - U.S. small business borrowing fell for the third straight month in May, data released on Thursday showed, a pullback that suggests economic growth prospects were already dimming before Britain's shock vote last week rocked global financial markets.

The Thomson Reuters/PayNet Small Business Lending Index fell to 128.6 in May from April's upwardly revised 129.5.

The PayNet index typically corresponds to U.S. gross domestic product growth one or two quarters ahead.

"You are going to see tepid GDP growth ... (and) the odds of a recession occurring are higher," said Bill Phelan, president of PayNet. He said the June 23 passage of Brexit, the U.K. referendum to leave the European Union, created more uncertainty for small companies as they grapple with fallout from the stronger dollar and the need to reassess the global economic outlook.

U.S. GDP probably rebounded in the second quarter after two tepid prior quarters, buoyed by consumer spending, estimates show.

But slowing momentum in the labor market, and tighter financial conditions after the Brexit vote, have convinced many traders that the Federal Reserve will keep policy on hold for many months to come.

Small business borrowing is a key barometer of growth because small companies tend to do much of the hiring that drives economic gains.

Loans more than 30 days past due rose in May to 1.54 percent, the highest in more than a year, separate data from PayNet showed.

PayNet collects real-time loan information such as originations and delinquencies from more than 325 leading U.S. lenders.

(Reporting by Ann Saphir; Editing by Andrew Hay)