The unemployment rate was unchanged at 4.3%, although there are questions over the reliability of the jobs figures from the ONS due to problems with gathering the data.
“After slowing steadily for over a year, growth in pay excluding bonuses increased slightly in the latest period driven by stronger growth in private sector pay,” said Liz McKeown, director of statistics at the ONS.
Private sector pay grew at an annual pace of 5.4%, the ONS said, while in the public sector it was 4.3%.
The Bank of England watches the pay and jobs data closely when making decisions on interest rates.
It has cut rates twice this year as inflation – which measures the rate at which prices are increasing – has fallen.
The Bank meets to discuss rates again this week, but it is not expected to make a further cut given the strength in pay growth.
“The latest UK jobs report provides yet more justification, if any were needed, for the Bank of England to keep rates on hold at its meeting this week,” said James Smith, developed markets economist at ING.
Mr Smith noted that the jump in wage growth was entirely down to the private sector.
“This matters for the Bank, because private sector pay trends tend to be more reflective of the wider situation in the jobs market than in the public sector,” he said.
Monica George Michail, associate economist at the National Institute of Economic and Social Research, said: “With low inflation, workers have been making real income gains.
“However, given the slowdown in recruitment activity and rising unemployment, we expect wage growth to slow in the coming months, although the rise in National Living Wage in April would exert some upward pressure.”