The government is set to announce wage increases for about one million workers in the public sector, the BBC understands.
Last year the PM announced plans to lift the 1% cap – in place since 2013 – but deals were only confirmed for some NHS workers, prison staff and police.
Other professions – including the armed forces, teachers and doctors – are now expected to see an increase.
The rises will be announced in a series of written statements to Parliament.
Sources told the Sun that staff will get pay rises of up 3.5% for 2018/19, although the BBC understands the average figure is likely to be lower.
The BBC’s political correspondent, Iain Watson, added that it is likely the increases will not be funded by the Treasury, with government departments having to use their own funds to meet them.
A new pay deal for the NHS was announced in March, promising a 6.5% increase over three years.
Workers voted on and agreed the deal in June, meaning 1.3 million will see the rise in their July pay packets.
However, the deal did not include doctors, dentists and senior leaders – which this announcement is expected to cover.
The cap for police and prison officers was also lifted last September, with unions accepting rises of 1% with a 1% bonus, and 1.7%, respectively for the following year.
Mrs May pledged that the costly plan to remove the cap – estimated at £4bn – would be rolled out over two years.
It was seen as a response to worries surrounding recruitment and retention, as well as to boost morale in the public sector.
But unions have been arguing for pay rises closer to 5% to make up for the austerity measures introduced by David Cameron’s government eight years ago.
The current level of inflation sits at 2.4% as of June 2018, meaning many of the rises could still fall below the figure.