* Dollar gains, boosted by recent economic data
* Oil prices slightly add to recent gains (Updates prices, adds comment, changes dateline from previous LONDON)
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 the renewed strength of the greenback on a recent string of better-than-expected economic data.
Despite the dollar strength, both Brent and U.S. crude added slightly to recent gains that have come on bets that OPEC and non-OPEC oil producers could reach an agreement on limiting production.
Sterling hit its weakest since 1985, pressured by a growing sense that Britain may be heading for a "hard" exit from the EU where it severs links to the single market in favor of total control over immigration.
The pound was down 0.8 percent at $1.2739, and near a three-year low at 87.78 pence per euro.
"It is now abundantly clear that access to the single market is not on (Prime Minister) Theresa May's list of top priorities and the market is realizing that ... there is more pressure for the pound in the weeks and months ahead," said UniCredit global head of FX strategy Vasileios Gkionakis.
London's FTSE cheered the idea of a weaker pound boosting firms' exports, rising 1.3 percent to the highest in more than a year and not far from a record peak.
On Wall Street traders withdrew from interest rate-sensitive sectors, with utilities, telecoms and real estate posting the largest percentage drops among S&P 500 sectors.
The Dow Jones industrial average fell 43.29 points, or 0.24 percent, to 18,210.56, the S&P 500 lost 5.5 points, or 0.25 percent, to 2,155.7 and the Nasdaq Composite dropped 1.92 points, or 0.04 percent, to 5,298.95.
The pan-European FTSEurofirst 300 index rallied 1.1 percent, while MSCI's gauge of stocks across the globe ticked down 0.1 percent.
Recent U.S. data indicating a strengthening manufacturing sector along with an upward revision to second-quarter gross domestic product has boosted bets of a Fed rate hike by year end. Traders now see above even odds of a rate increase in December.
Asian shares finished modestly higher overnight, led by a 0.8 percent rise from Japan's Nikkei as the stronger dollar muscled the yen lower.
Oil prices edged up, with Brent hitting four-month highs on a rally inspired by OPEC plans to tighten output before pulling back as the stronger dollar weighed.
U.S. crude was up 0.2 percent at $48.90 a barrel and Brent last traded at $51.12, up 0.5 percent on the day.
The dollar index, which tracks the currency against a basket of major peers, rose 0.5 percent to 96.191. The greenback strengthened to 102.780 yen and $1.1184 per euro.
U.S. Treasury yields rose. Benchmark 10-year notes fell 12/32 in price to yield 1.6655 percent, up from 1.624 percent on Monday.
Spot gold prices fell $36.14 or 2.8 percent, to $1,275.31 an ounce.
Additional reporting by Barani Krishnan and Richard Leong; Editing by Meredith Mazzilli