By William Schomberg

LONDON (Reuters) -A key measure of British wages matched its highest growth rate on record but there were also some signs that the inflationary heat in the labour market is subsiding, offering the prospect of some relief ahead for the Bank of England.

The 7.3% increase in basic earnings in the three months to May matched the reading in the three months to April - which was revised up from an initial estimate of 7.2% - and also the second quarter of 2021, the Office for National Statistics said.

Economists polled by Reuters had forecast a 7.1% rise.

Sterling touched a 15-month high against the dollar as it rose by 0.3% on the day and also gained moderately against the euro after the data.

But the figures also suggested that the labour market was becoming less tight as the unemployment rate unexpectedly rose to 4.0% from 3.8% in the three months to April and vacancies extended their run of falls to their lowest since mid-2021.

The yields on two-year British government bonds, which are sensitive to speculation about interest rates, fell by around three basis points in early trade.

"The labour market became less tight in May and there are some signs of momentum in wage growth slowing a bit," Ashley Webb, an economist with Capital Economics, said.

"But with wage growth still well above the levels consistent with the 2% inflation target, this won't ease the Bank of England's inflation fears significantly."

The BoE is monitoring pay growth closely as it assesses how much inflationary pressure remains in Britain's economy even after its 13 back-to-back interest rate increases.

Governor Andrew Bailey said on Monday wage increases as well as prices charged by companies were rising too fast and he vowed to "see the job through" on fighting an inflation rate that at 8.7% is running higher than in any other big rich economy.

Samuel Tombs, with Pantheon Macroeconomics, said the BoE might see enough signs of a slowdown in the data to allow it to halt its run of rate increases soon, although probably not when it makes its next monetary policy announcement on Aug. 3.

"For now, wages still are rising too quickly for the MPC to tolerate on an ongoing basis," he said. "But it always has taken a little time for changes in labour market slack to influence wage growth and some leading indicators remain encouraging."

Annual pay growth including bonuses sped up to 6.9%, the fastest on record excluding the coronavirus pandemic period when government job subsidies distorted the data, the ONS said.

(Reporting by William Schomberg; editing by Sachin Ravikumar, Kate Holton and Christina Fincher)