The unemployment rate in the U.K. remained unchanged in the three months to May, signaling that the country’s labor market remained tight even as economic growth slowed.

The U.K.’s unemployment rate stood at 3.8% in the three months through May, unchanged from the preceding three-month period, according to data from the Office for National Statistics published Tuesday.

Employment continued to increase, with the number of payrolled employees rising by 31,000 in June to a total of 29.6 million.

Job vacancies rose again from April to June to 1.29 million but the rate of growth continued to weaken.

“With demand for labour clearly still very high, unemployment fell again, employment rose and there was another record low for redundancies,” the ONS said.

Wage growth remained elevated. Average weekly earnings in the three months to May excluding bonuses rose 4.3% on year, accelerating from the 4.2% increase registered in the preceding three-month period. Adjusted for inflation, earnings without bonuses decreased 2.8%.

Excluding bonuses, real pay is currently dropping faster than at any time since records began in 2001, the ONS said.

Write to Xavier Fontdegloria at xavier.fontdegloria@wsj.com