Sterling won a boost after Conservative leader May declared late Tuesday that she would look for another Brexit delay and softened her position to try and avert a messy no-deal divorce from the European Union next week.
Labour leader Jeremy Corbyn has consistently called for Britain to remain in a customs union with the bloc, while the government has so far ruled this out saying Britain should have an independent trade policy after Brexit.
"The announcement was win-win for the pound," Oanda analyst Craig Erlam told AFP.
"Not only did May re-affirm her opposition to no deal, she's technically opened the door to a softer Brexit. I say technically because a lot now has to happen for that to be delivered, including the Conservatives and Labour working together towards an uncharacteristic compromise."
However, he added: "If this fails, I struggle to see how she recovers; it very much feels like a last-ditch, desperate gamble."
- 'Last throw of dice' -
AxiTrader analyst James Hughes meanwhile questioned why May had waited this long to hold discussions with Corbyn.
"This feels very much like the last throw of the dice, with the argument being that cross-party talks should have been the first throw of the dice," Hughes told AFP.
"The deadlock, political infighting and MPs' inability to make a decision has led to both the process and the country to a certain degree becoming a laughing stock.
"Continuous votes on outcomes that the majority know will be rejected by the EU anyway are wasting time, and it's only now that we are taking the prospect of no deal seriously enough."
However, sterling's gains were capped Wednesday by a gloomy survey showing that Britain's vital services sector shrank in March for the first time in almost three years, with activity slammed by Brexit turmoil and flat economic growth.
- 'Glass-is-half-full mentality' -
Trading on Wall Street opened higher on Wednesday, despite new data showing that hiring in the US private sector slowed for the second month in a row in March -- hitting its slowest pace in 18 months.
The monthly data from payrolls firm ADP comes two days before a more closely watched government report on employment.
"Businesses are hiring cautiously as the economy is struggling with fading fiscal stimulus, the trade uncertainty, and the lagged impact of Fed tightening," said Mark Zandi, chief economist at Moody's Analytics, which jointly produces the report.
Meanwhile, European and Asian stock markets advanced Wednesday as a report said China and the US were closing in on a deal to end their long-running trade row.
"Clearly, the stock market continues to look at those negotiations with a glass-is-half-full mentality," said Briefing.com analyst Patrick O'Hare.