* Dollar gains, boosted by recent economic data
* Oil prices rise late after data (Updates to U.S. market close)
By Rodrigo Campos
NEW YORK, Oct 4 (Reuters) - Sterling slumped to a 31-year low versus the U.S. dollar on Tuesday as concerns over Britain's separation from the European Union were compounded by renewed strength of the greenback on a recent string of better-than-expected economic data.
Both Brent and U.S. crude oil rose late despite the dollar's strength on a surprise U.S. crude stockpile drawdown.
Sterling hit its weakest since mid-1985, hit by a growing sense that Britain may be heading for a 'hard' exit from the EU in which it severs links to the single market in favor of total control over immigration.
Such a move could crimp London's ability to remain a global financial hub.
The pound was down 0.9 percent at $1.2722, having hit a low of $1.2715, and at a three-year low versus the euro at 88.02 pence.
"Everything people are hearing from the UK is not positive for its currency," said Paresh Upadhyaya, director of currency strategy at Pioneer Investments in Boston.
London's FTSE cheered the idea of a weaker pound boosting firms' exports, rising 1.3 percent to its highest in more than a year and within half a percentage point of its record high hit in April 2015.
On Wall Street traders withdrew from interest-rate-sensitive stocks as recent U.S. data including a strengthening manufacturing sector and upward revision to second-quarter gross domestic product has boosted bets of a rate hike by the Federal Reserve before the year ends. Traders now see above-even chances of a rate increase in December.
Rate-sensitive stocks like utilities, telecoms and real estate posted the largest percentage drops among S&P 500 sectors. Broadly, U.S. stocks were also weighed by the uncertainty over Britain's divorce from the EU.
"Clearly there has been some reverberation from across the pond in terms of the prospect for a slightly more disorderly UK separation from the EU," said Bill Northey, chief investment officer for the private client group at U.S. Bank in Helena, Montana.
The Dow Jones industrial average fell 85.4 points, or 0.47 percent, to 18,168.45, the S&P 500 lost 10.71 points, or 0.5 percent, to 2,150.49 and the Nasdaq Composite dropped 11.22 points, or 0.21 percent, to 5,289.66.
The pan-European FTSEurofirst 300 index rallied to close up 0.9 percent, while MSCI's gauge of stocks across the globe ticked down 0.2 percent, weighed by Wall Street's decline.
Asian shares had finished modestly higher overnight led by a 0.8 percent rise from Japan's Nikkei. Nikkei futures were up nearly 1 percent.
Crude oil prices jumped in post settlement trading after a surprise large draw in inventories in the United States. Crude stockpiles tumbled unexpectedly last week as imports dropped, data from the American Petroleum Institute showed.
U.S. crude was up 0.8 percent at $49.19 a barrel and Brent last traded at $51.27, up 0.8 percent on the day.
The dollar index, which tracks the currency against a basket of major peers, rose 0.5 percent to 96.137. The greenback climbed to 102.88 yen and $1.12 per euro.
U.S. Treasury yields rose. Benchmark 10-year notes fell 19/32 in price to yield 1.6899 percent, up from 1.624 percent on Monday.
Spot gold prices fell $41.53 or 3.2 percent, to $1,269.92 an ounce. (Additional reporting by Barani Krishnan, Noel Randewich and Richard Leong; Editing by Meredith Mazzilli and James Dalgleish)