According to a report from the Office for National Statistics (ONS), the number of job vacancies hit 953,000 in the three months to July.
The unemployment rate fell to 4.7% in the three months to June, while the annual growth in average pay was 7.4%.
However, the ONS urged caution in reading too much into the rise in wages as the figures are being compared to the same time last year when millions of people were on furlough and were not being paid their full wage.
The number of people on payroll has now grown over half a million in the past three months, regaining about 80% of the fall seen at the start of the pandemic.
While the chancellor welcomed the figures as "promising", analysts warned that the unemployment figures would rise as the furlough scheme continued to be phased out. But the peak unemployment rate is on course to be significantly lower than had been expected last year.