Against a basket of currencies, sterling was marginally higher, falling half a percent against the resurgent dollar but gaining around the same amount against the euro, having fallen sharply on Monday, the year's first proper day of trading.

The PMI index of sentiment among construction purchasing managers jumped to 57.8 in December, way above the 50 reading that separates economic expansion from contraction and compared to a consensus forecast of 56.0.

That gave sterling a small boost and some said there may now be more support for the currency after a surge in Brexit-related derivative bets against it in December.

"The heavy selling over December has turned to profit taking by hedge funds and real money," said Citi strategist Richard Cochinos in the latest detailed report on flows by the currency world's single biggest banking player.

"We are cautious not to call an end to the GBP lower trend, but our flows suggest the GBP weaker view is consensus and moves lower may be more difficult in the short run."

Still, a number of banks have recommended selling the currency this year given the risk of a destabilising referendum on whether to stay in the European Union.

"Shaky is the only way I can put it on the pound," said a dealer with one bank in London. "There's no sign of anyone prepared to buy heavily into these bouts of weakness at the moment."

Sterling traded at $1.4656, having hit a low of $1.4638. It stood at 73.19 pence per euro, pushing it to 90.6 on the Bank of England's trade-rated index from 90.4 on Monday.

Prime Minister David Cameron has promised a vote on whether to stay in the EU by the end of 2017, but last month hinted it could come this year. Many market players are betting it will happen as soon as June.

With the outcome of the ballot unclear, that is likely to spell considerable uncertainty and volatility.

Sterling had rallied into the middle of last year, hitting a 7-1/2-year high on a trade-weighted basis in August on expectations the Bank of England would raise rates soon after the U.S. Federal Reserve, which made its move last month.

But an EU referendum could tie the Bank's hands for a portion of the year, while inflation remains stuck around zero despite robust sentiment data like Tuesday's PMI.

"Sterling's consistent underperformance over the last month is hard to rationalise," said Adam Cole, Head of G10 FX Strategy at RBC in London.

"Economic data have on balance been close to expectations and rate expectations have been rising. For now, we are not prepared to fight the solid negative trend in GBP, though our medium term outlook remains positive."

(Editing by Ruth Pitchford)

By Patrick Graham