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.
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' -
The move, which followed a long cabinet meeting on Tuesday, angered Brexit hardliners in May's party as it opens the possibility of Britain seeking closer economic ties with the EU after leaving.
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 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.
The purchasing managers' index (PMI) for services fell from 51.3 in February to 48.9 in March, according to IHS Markit, which compiles the data. That was the lowest level since July 2016, which was one month after Britons voted in favour of leaving the European Union.
- 'Detrimental impact of Brexit' -
The figure below 50 indicates that the service sector, which accounts for some 80 percent of British gross domestic product, is in contraction.
"Despite the new market optimism surrounding the Brexit process, the UK growth story has since come into focus, with a sharp decline in the services PMI taking the sector into contraction for the first time in almost three years," noted IG analyst Joshua Mahony.
"A decline in business activity and new orders has highlighted the detrimental impact of the ongoing Brexit uncertainty, with respondents reporting anxiety over how economic underperformance is holding back household spending."
Investors built on recent gains, with optimism given an extra boost by a report in the Financial Times saying Beijing and Washington were on course for a historic agreement.
Expectations that the world's top two economies will eventually sign a deal has been a key driver of a global equities rally this year and the FT article adds to the general sense of hope.
It comes after better-than-expected factory data out of China and the US that eased worries about growth in the global economy, while a dovish turn from central banks has also provided support.