The British pound was steady on Monday, holding above $1.25 against the dollar before key labour market data on Tuesday that could leave the door open for the Bank of England to cut interest rates as soon as its June meeting.

The pound was last up less than 0.1% against the dollar at $1.2529, having fallen 0.2% against the U.S. currency last week. Sterling was down 0.1% at 86.06 pence per euro .

The BoE last week left its Bank Rate unchanged at a 16-year high of 5.25%, but Governor Andrew Bailey said he was optimistic that inflation was moving in the right direction.

In a further signal that rate cuts were coming into view, a second member of the nine-person rate-setting Monetary Policy Committee (MPC), Deputy Governor Sir Dave Ramsden, joined Swati Dhingra in voting to lower borrowing costs.

"The messaging went about as far as it could to signal that the MPC could cut as soon as June if the data cooperate," said Goldman Sachs strategists in a note.

Money market traders were not wholly convinced of a move in June, pricing in around a 55% chance that the BoE makes a quarter-point cut to the Bank Rate next month.

Markets were now turning their attention to labour market data on Tuesday, where strong wages could dampen expectations for easier monetary policy.

"There are still some risks that we see another strong figure in wages and that will keep markets a bit more cautious in pricing in more rate cuts," ING FX strategist Francesco Pesole said.

Economists polled by Reuters expect average weekly earnings to have increased 5.5% in the three months to March, down from 5.6% the month before.

It's the first of two labour market reports and two inflation releases before the BoE's June meeting.

"The consensus is for another decent fall ... which is the right direction to keep investors enthused about an interest rate cut in either the June or August meetings," said Kyle Chapman, FX analyst at Ballinger Group.

Analysts were also waiting for speeches from some of the more hawkish members of the MPC, with Huw Pill (Tuesday), Meg Greene (Thursday) and Catherine Mann (Friday).

(Reporting by Samuel Indyk; Editing by Alex Richardson)