Rising vacancies and falling unemployment fail to push firms into raising wages.
Wage growth has slowed in the UK to put a squeeze on living standards despite unemployment falling to its lowest level for more than 40 years.
The fall in pay growth to 3.3% on the year in the three months to March, from 3.5% in the three months to February, also came as the buoyant labour market recorded a rise in employment to a new high of 32.7 million. The jobless rate fell from 3.9% to a record 3.8%, the lowest since 1974.
However, analysts said this trend had not driven employers to increase wages to levels seen before the financial crisis.
Brexit-related uncertainty was blamed for a rise in self-employment, which returned to its record high of 15.1% of all jobs, last seen in 2017.
Much of the tumbling rate of female unemployment is down to tougher welfare rules that push women with young children back into the labour market. Pension rule changes that force women nearing retirement to work longer have also had an impact.