By Barani Krishnan

NEW YORK (Reuters) - Oil prices rose 3 percent on Monday, settling higher for a second straight day, after polls showing a lower likelihood of Britain leaving the European Union while U.S. gasoline surged 5 percent in anticipation of peak summer driving demand.

Data from market intelligence firm Genscape pointing to a drawdown of 568,213 barrels at the Cushing, Oklahoma delivery base for U.S. crude futures in the week to June 17 was also supportive, said traders who saw the numbers.

A Reuters poll also showed total U.S. crude stockpiles likely fell 1.9 million barrels last week, declining for a fifth straight week.

U.S. gasoline futures <RBc1> jumped 5 percent, their most in six weeks, as the rally in crude extended to refined oil products. Traders cited speculative buying in gasoline ahead of the July 4 Independence Day weekend when summer driving usually hits a high in the United States.

"Demand has been very strong year-over-year for gasoline and coupled with the peak driving season just ahead of us, we got a strong bid today that should continue in the short term," said Chris Jarvis, analyst at Caprock Risk Management in Frederick, Maryland.

Crude futures rose after three opinion polls ahead of Thursday's vote on Britain's future in the EU showed the 'Remain' camp recovering some momentum, although the overall picture was of an evenly split electorate. Traders said Britain's exit, or "Brexit," could cause economic turmoil to Europe and beyond.

The British pound climbed 2.3 percent to $1.4685 against the dollar. A weaker dollar makes commodities denominated in the greenback more attractive for other currency holders.

Brent crude futures' front-month contract, August, settled up $1.48, or 3 percent, at $50.65 a barrel. The contract has risen 7 percent since Thursday's settlement, after falling 10 percent in six previous sessions.

U.S. crude's West Texas Intermediate (WTI) futures gained $1.39, or 2.9 percent, at $49.37 a barrel for the July front-month. But the contract, which expires on Tuesday, was barely traded, transacting a tenth of average daily volume. Investors flocked instead to August WTI, the new front-month from Wednesday, which settled up 3 percent at $49.96.

Analysts said oil prices should stay firm as long as a Brexit looked unlikely, although a strong rally may be difficult absent fresh supply outages.

"We are not expecting sustained crude price strength back to above the $50-51 area in either WTI or Brent as fundamentals appear to be undergoing a very gradual shift back toward the bearish side," said Jim Ritterbusch of Chicago-based oil markets consultancy Ritterbusch & Associates.

(Additional reporting by Amanda Cooper in LONDON; Editing by Marguerita Choy)