Pay expectations in the public sector rose to 4%, the highest recorded by the CIPD, from 3.3%.
Growth in earnings excluding bonuses - which typically runs slightly higher than pay settlements - was an annual 7.3% in the three months to May.
The CIPD said businesses were also becoming more likely to match or exceed pay offers by rivals for their staff.
However, almost a third of employers believed counteroffers were ineffective at keeping staff.
"For some employers, counteroffers may only be valuable as a short-term option and ... employees will move if wider aspects of the job, such as workload, autonomy and environment, don't meet their expectations," the CIPD said.
Persons:
Rishi Sunak, BoE, David Milliken, William Schomberg
Organizations:
Chartered Institute, Personnel, Private, of England, Data, Thomson