Mr Morgan, the ONS's director of economic statistics, said that basic pay "is growing at its fastest since current records began".
Mr Morgan told BBC Radio 4's Today programme that real pay growth, when taking into account the rate of inflation, "is still falling a little".
Figures show that, taking into account the Consumer Prices Index (CPI) measure of inflation, average regular pay fell by 0.6%.
"The fall in employment in the three months to June and further rise in the unemployment rate will be welcomed by the Bank of England as a sign labour market conditions are cooling, " said Ruth Gregory, deputy chief UK economist at Capital Economics.
Ms Mason said the company had increased its wages to fill shifts left vacant by employees who, following Covid, decided they wanted a better work-life balance and have chosen to work fewer days.
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