LONDON, May 14 (Reuters) - Sterling fell on Tuesday after Bank of England chief economist Huw Pill said the central bank might be able to consider cutting interest rates over the summer.

Pill's remarks came after data showed that British wages grew by more than expected in the first three months of the year, but other figures suggested the labour market is losing some of its inflationary heat, keeping the BoE on alert about when to cut interest rates.

Sterling fell as much as 0.4%, before trimming some of those declines, after the BoE policymaker's remarks in an online presentation organised by the ICAEW, an accountancy body.

"I think it's not unreasonable to believe that through the summer we will begin to see enough confidence in the decline in persistence that Bank Rate will come into consideration," Pill said.

Last week, he voted with the majority of the BoE's Monetary Policy Committee to keep interest rates at a 16-year high of 5.25%.

Regular wages, excluding bonuses, grew by 6.0% in the first three months of 2024 compared with the same period a year earlier. Economists polled by Reuters had forecast wage growth of 5.9%.

Unemployment rate rose to 4.3% in the period, however, its highest since the three months to July 2023. Vacancies fell for the 22nd time in a row in the three months to April.

"This data has not shifted the dial for UK rate expectations. The market is still expecting the first rate cut to happen either in June or August," said Kathleen Brooks, research director at XTB.

"April’s increase in the minimum wage means that next month’s wage and jobs data could be more useful for the BoE. We also think that CPI data due next week will have a bigger impact on UK rate cut expectations," she said.

Money markets continued to price in around a 50% chance of a cut in June, according to LSEG data. They see a 75% chance of a cut in August.

The pound was last 0.12% lower at $1.2543. Against the euro, it was down 0.16% to 86.05 pence, having touched a one-week high against the single currency earlier in the day.

(Reporting by Joice Alves in London, editing by Ed Osmond)