(Recasts after sterling halves day's gains)
By Patrick Graham and Jemima Kelly
LONDON, Oct 12 (Reuters) - Sterling rebounded from a record low in trade-weighted terms on Wednesday after Britain's prime minister said she would give lawmakers some scrutiny of the Brexit process and would seek "maximum possible access" to Europe's single market.
The pound surged by as much as 1.5 percent against the dollar and the euro on the moves by May concerning a parliamentary debate initially read as handing MPs a substantial opportunity to undermine the "hard Brexit" scenario that has scared investors over the past fortnight.
A "hard Brexit" is seen as leaving Britain out of European Union's single market and threatening London's role as a major financial centre.
The gains eased, however, around midday in London when May and her Brexit minister, David Davis, sounded some less concessionary notes in a pair of appearances in parliament.
To many dealers and analysts the gains for the pound still looked like just a brief pause after four days which have sent the currency to its weakest on record, according to the trade-weighted index run by the Bank of England.
Against the dollar alone, it remains, at around $1.21, some way from an all time low of just above parity hit in 1985.
"You could say there was some kind of backtracking to at least allow parliament some greater profile," said Lee Hardman, currency economist with Bank of Tokyo-Mitsubishi UFJ in London.
"But you would have to be very optimistic to think that it will have a big impact on the process, to expect that it means they will ultimately give parliament greater say."
Sterling was just 0.8 percent higher, almost halving its gains on the day to stand just over a cent above Tuesday's lows of $1.2090.
The currency has plunged almost 18 percent against the dollar since Britain's shock vote in June to leave the European Union.
After a brief period of stability the sell-off has worsened again in the past fortnight on a series of signs that the government would prioritise controls on immigration over access to the European single market.
May moved late on Tuesday to appease some lawmakers in her ruling Conservative Party by allowing a motion proposed by the opposition Labour Party for a "full and transparent debate" on how the government will enact the public vote to leave the EU.
But while that agreed to demands for parliament to debate her government's plans, it also ruled out letting it vote on triggering the formal Brexit procedure.
Brexit Minister Davis also banged home the message that it is the government that will decide when to trigger Article 50, the formal legal process for leaving the European Union, before beginning exit negotiations.
"The move this morning was on May's comments but largely because they were initially read as something they weren't: she is not really changing stance, parliament will not be able to veto a hard Brexit," said the head of hedge fund sales at one large international bank in London.
The major banks have stuck to forecasts of about $1.20-1.25 for sterling, but an apparently computer-trader-driven flash crash to as low as $1.1491 on Friday has left some wondering if a fall near to parity is likely.
"What is clear is there is a lack of interest to buy sterling from clients. It is hard to see who is going to come in and support it from here," said the hedge fund sales head. (Additional reporting by Patrick Graham; Editing by Jeremy Gaunt)