Yet businesses also said they were hiring at a rate not seen for at least the last quarter century. The IHS Markit/Chartered Institute of Procurement and Supply (Cips) UK services purchasing managers' index (PMI) reached 55 in August. It is a long way off from May's 62.9 and a slowdown from 59.6 in July.
Economists had predicted a score of 55.5 according to a consensus from Pantheon Macroeconomics. Yet the figure still implies that the sector is growing – any score above 50 is positive.
"The service sector lost momentum for the third consecutive month as the impact of looser pandemic restrictions faded in August," said Tim Moore, economics director at IHS Markit, which compiles the survey.
The rate of job-creation rose, beating the previous survey record that was set in June 2014. Meanwhile, there are not enough candidates to fill all the jobs, which is pushing up wages.
This rise in pay packets is pushing up costs for the services companies, and they are in turn passing on some of this to their customers, the survey found.
The shortage of labour – and the number of staff who have to self-isolate because of Covid-19 – has also put pressure on the sector, leading to unfinished projects. Businesses also reported problems in their supply chains.
"Many businesses suffered constraints on growth due to staff shortages, self-isolation rules, and stretched supply chain capacity," Mr Moore said. "Service- providers signalled the sharpest rise in employment since data collection began 25 years ago.
"Additional staff recruitment typically reflected efforts to return workforce numbers to pre-pandemic levels after widespread job cuts last year. Many survey respondents commented on long wait times to fill vacancies and an unexpectedly high staff turnover as the UK economy reopened."
Duncan Brock, group director at Cips, said: "With the third monthly fall in a row, new order growth failed to impress and work from overseas barely rose.
"Brexit continued to make its mark and supply shortages and logistics difficulties will pile on the pressure in the coming months, but service companies remained buoyant about future opportunities."
James Bentley, director of Financial Markets Online, commented: “This is the clearest sign yet that Britain’s booming services sector is being tripped up by spiking cost inflation and staff shortages.
“With consumer demand easing off only a touch from its initial post-lockdown surge, output is being dragged down in large part because many service businesses just don’t have the staff they need to get the work done.
“This has unleashed a wave of hiring, with August’s PMI survey clocking the biggest jump on record in service sector recruitment. Employers are increasing wages rapidly in a bid to woo recruits, and the resulting cost pressures are slicing into their profit margins.
“Despite these growing pains and the slide in output, business confidence in Britain’s dominant industrial sector remains high.
“With the Bank of England turning a blind eye to the mounting inflationary pressure, the likelihood of an imminent interest rate rise remains slim, keeping sterling largely flat after an nondescript week against both the euro and the dollar.”