* Graphic: sterling and gilt yields bit.ly/2dgAXn1
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv
By Marc Jones
LONDON, Jan 18 (Reuters) - Sterling dropped back on Wednesday after making its biggest one-day gain since at least 1998 on Tuesday as Prime Minister Theresa May outlined Britain's hopes for its exit from the European Union.
With May due to speak again later, sterling sliced 0.7 percent off Tuesday's 3 percent surge against the dollar, leaving it at $1.2329. It topped out at $1.2416 the previous day, having been as low as $1.1983 on Monday.
In a speech, May confirmed that she planned to take Britain out of the EU's single market, but cheered currency markets by including promises to let parliament have a say on its Brexit deal and give firms time to transition to the new setup.
Asset manager GAM's group head of multi asset portfolios Larry Hatheway said the message had been well-received because it sought solutions rather than a confrontational approach. But there remains huge uncertainty over where the talks will lead.
"I don't think sustained rallies in the pound are likely," he said. "My sense is that we are going to challenge the $1.20 level before too long again, and 1.15 is not out of the question, but there won't be the kind of weakness (for the pound) that we saw in the second half of last year."
Britain's Brexit minister said in a radio interview that other EU countries had welcomed May's comments on Tuesday and that he and his colleagues would seek a trade deal where customs arrangements were "as frictionless as possible".
In line with the day's broader pullback, sterling also dipped 0.5 percent against the euro to leave it at 86.76 pence per euro. It had hit 86.27 pence on Tuesday after weakening to as little as 88.53 pence on Monday.
Gauges of expected sterling volatility also nudged back up, with one-week options at 7.8 percent. That was well below the 17.5 percent level it jumped to at the start of the week.
British wage and unemployment data are due at 0930 GMT. (Editing by Catherine Evans)