The latest unemployment figures showed a decrease in claimant count jobless of 20,800 in June from May.
This equates to a 1.4% decline and is the fifth consecutive monthly reduction.
Unemployment on the internationally comparable ILO measure fell by a similar amount with a reduction of 34,000 in the three months to May over the previous non-overlapping quarter. Also a 1.4% reduction.
Employment data was also positive, with 160,000 additional individuals employed in the three months to May. This was an increase of 0.6%, the largest rise since August 2006.
A large driver of this trend however was a record 148,000 increase in the number of people employed on a part-time basis.
The cebr's Owen James said clearly underemployment and spare capacity remained ingrained in the system.
This helped explain why average weekly earnings (including bonus payments) remained sluggish in May.
Although these rose by 2.7% in the three months to May compared to the same period last year, they were down from 4.1% last month and 4.3% in March. The equivalent figure for the public sector was 3.2%, the lowest figure since June 2009.
Taken at face value it may appear that there has been a halt in the deterioration of the labour market, but ignoring the impending cut backs in the public sector would be languid.
Like the Office of Budget Responsibility the cebr said it saw public sector employment falling by approximately 600,000 between 2012 to 2015.
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