Sterling has fallen 1% this month as deadlocked cross-party  talks exposed deep political divisions over how, when and even if Brexit should take place.

May's spokesman said late on Tuesday she planned to put forward her thrice-rejected Brexit deal in the week beginning June 3, to try to secure an agreement before lawmakers go on summer holiday.

Speculation is growing that May will soon be ousted and that is weighing on the pound.

"Failure to pass the deal [in June] could well see May finally step down, opening the door for a more eurosceptic prime minister. The pound risks $1.2800 in the near term," said Petr Krpata, an FX strategist at ING in London.

Sterling was trading 0.1% higher at $1.2916 and flat against the euro at 86.80 pence. It has fallen for seven consecutive days against the dollar despite mostly  solid economic data in Britain in recent months.

The worry for investors is that months of inventory stockpiling by British companies before Brexit will show up this quarter.

British employment data on Tuesday showed wage growth in the quarter ending March was lower than expected, signalling the possible start of a turbulent period for the broader economy.