* World FX rates in 2019 http://tmsnrt.rs/2egbfVh
* Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Adds details, quotes, graphic)
LONDON, March 26 (Reuters) - Sterling bounced a quarter of a percent on Tuesday after two eurosceptic lawmakers indicated they could agree to support British Prime Minister Theresa May's EU withdrawal deal rather than risk the UK parliament cancelling Brexit altogether.
The comments follow Parliament's move to wrest control of the Brexit process for a day. Its action has raised expectations that lawmakers can end an impasse on Britain's European Union exit, with the possibility of a longer Brexit delay or a second referendum.
Lawmakers will now vote on Wednesday on a range of options, giving parliament a chance to indicate whether it can agree on a deal with closer ties to Brussels -- and then try to push the government in that direction.
Jacob Rees-Mogg, the leader of a eurosceptic faction of May's Conservative Party, hinted he could scale back opposition to May's deal which has already been crushingly rejected twice by lawmakers. Passing the deal would rule out the risk of leaving the EU without any transition arrangements.
Another Conservative lawmaker, Michael Fabricant, said he had arrived at the same conclusion as Rees-Mogg.
The pound, which had languished mostly in negative territory below $1.32, rose 0.3 percent to as high as $1.3251 after Rees-Mogg's comments. Against the euro it firmed 0.4 percent to 85.43 pence
"Comments by Jacob Rees-Mogg show he is formally acknowledging he may accept May's deal," MUFG strategist Lee Hardman said. "This increases the likelihood that May's deal could pass."
But Hardman added: "His support by itself can't tip the balance in favour of the deal passing ... The numbers still don't stack up."
The pound is unlikely to rally much further however. May has stressed she will not implement any Brexit proposal that breaks her pledge of a clean break with the EU. That means she could call an election, an outcome also favoured by the opposition Labour Party.
Bookmaker Ladbrokes has slashed the odds of a June election to 7/2, from 6/1 before Monday's vote in parliament.
"The key question will be whether MPs can rally together and agree on a majority out of the several options that will be presented. Even if there was a majority formed, it is unlikely to be implemented by Theresa May at this stage," said Mohammed Kazmi, portfolio manager at UBP.
The muted sterling reaction to Monday's vote was because of "the possibility of a longer extension to Article 50 and general elections taking place," Kazmi added, referring to the Brexit negotiating period.
The uncertainty drove up demand for protection against sterling swings.
Implied volatility -- a gauge of expected swings in the currency -- eased a touch, however, though the one-month contract, encompassing the crucial April 12 new date of Brexit, is close to 3-1/2 month highs hit on Monday.
The premium for options which protect against sterling losses over gains against the dollar -- risk reversals -- touched their highest levels late on Monday since just after the 2016 Brexit referendum.
"Currency markets are not going to boost GBP significantly until no-deal risk is dealt with," said Jeremy Thomson-Coo, head of currency strategy at WorldFirst
Meanwhile data highlighted the toll the prolonged uncertainty is taking on the British economy, with banking industry group UK Finance reporting mortgage approvals at the lowest level in almost six years.
The run of weak UK data, together with a general lurch towards dovishness by the U.S. Federal Reserve and other central banks, have seen money markets almost price out any chance of a Bank of England interest rate rise in 2019, another factor that's likely to pressure sterling.
These factors have pushed yields on 10-year British government bonds well below 1 percent, the lowest since Sept 2017.
(Reporting by Sujata Rao; additional reporting by Richard Pace; graphic by Saikat Chatterjee; Editing by Catherine Evans)