By Noel Randewich

(Reuters) - Wall Street dropped for a fourth straight session on Tuesday as central bank policymakers weighed the health of the U.S. economy and investors worried about an upcoming vote in Britain on whether to leave the European Union.

Investors launched a late-day rally but the major indices still ended with losses. The U.S. Federal Reserve began its two-day meeting to decide whether the U.S. economy has recovered enough to absorb an interest rate hike.

While traders have discounted a rate increase this month, they will parse Fed Chair Janet Yellen's comments on Wednesday for clues on the health of the economy and the trajectory of hikes.

Among banks that tend to benefit from higher interest rates, Wells Fargo <WFC.N> and JPMorgan Chase <JPM.N> took a hit and weighed most on the S&P 500.

Adding to angst on Wall Street, recent opinion polls indicated growing support for Britain's exit from the European Union, creating a rush by investors to safe-haven assets like gold and the yen.

The CBOE Volatility index <.VIX>, or Wall Street's fear gauge, reached its highest in over three months.

Over the past four sessions, the S&P 500 has lost 2 percent.

"We're trading on the Brexit polls," said John Canally, chief economic strategist for LPL Financial. "Markets are better priced for it today than a week ago, but they are still not fully priced for a 'leave' vote."

Four of the 10 major S&P sectors lost ground, with financials <SPSY> falling 1.45 percent. Wells Fargo declined 2.27 percent and JPMorgan Chase lost 1.88 percent.

Traders see virtually no chance of a rate hike on Wednesday, according to CME Group's FedWatch tool. They are pricing in a 21 percent chance of a rate hike in July, a 40 percent chance in September and a 59 percent chance in December.

"The focus will be on the number of hikes Federal Reserve participants see through the year," said Bill Northey, chief investment officer at Private Client Group of U.S. Bank.

One bright spot was a better-than-expected 0.5 percent rise in U.S. retail sales in May.

The Dow Jones industrial average <.DJI> fell 0.33 percent to end at 17,674.82 points and the S&P 500 <.SPX> lost 0.18 percent to 2,075.32.

The Nasdaq Composite <.IXIC> declined 0.1 percent to 4,843.55.

About 7.4 billion shares changed hands on U.S. exchanges, above the 6.7 billion average for the past 20 trading days, according to Thomson Reuters data.

Declining issues outnumbered advancing ones on the NYSE by 1,988 to 1,044. On the Nasdaq, 1,719 issues fell and 1,122 advanced.

The S&P 500 index showed 11 new 52-week highs and six new lows, while the Nasdaq recorded 24 new highs and 78 new lows.

(Additional reporting by Ann Saphir in San Francisco and Yashaswini Swamynathan in Bengaluru; Editing by Meredith Mazzilli and Nick Zieminski)