LONDON (Reuters) - British companies kept hiring staff last month after a brief lull around June's European Union membership referendum, but pay growth for temporary workers slowed, a monthly survey of recruitment agencies showed on Friday.

The Recruitment and Employment Confederation (REC) said businesses hired permanent staff last month at a similar rate to August after cutbacks in June and July, while a separate YouGov/Cebr survey of businesses showed a rebound in morale.

But pay rates for temporary staff rose at the slowest pace in more than three years, pointing to a risk that higher inflation could catch up with wage growth, the REC said.

"We hope the government will address this issue ... with fiscal stimulus. This should help to settle the nerves so that employers feel confident enough to keep hiring," REC policy director Tom Hadley said.

The REC also said Britain faced skill shortages and would continue to need workers from overseas in sectors such as engineering and healthcare.

"The business community must have a role in developing an immigration model that strikes the right balance," Hadley said.

Prime Minister Theresa May pledged earlier this week to curb migration from the EU. One of her ministers proposed requiring firms to state how many immigrants they employed and take steps to train more British staff.

A monthly survey by polling company YouGov and economics consultancy Cebr showed business sentiment had returned to the level seen in May and June, after a sharp fall in July and a partial recovery in August.

YouGov's Stephen Harmston said sentiment could deteriorate once businesses had taken on board May's emphasis on curbing EU migration in her speech at this week's Conservative Party conference, rather than on maintaining full access to the bloc's single market.

"We will have to wait to see whether the rebound in confidence is itself hard and resilient to such talk or whether it is soft and causes another spasm of panic among organizations," Harmston said.

"Whichever it is, these figures could well represent the end of the pre-Brexit honeymoon period," he added.

The YouGov/Cebr poll of 500 'business decision makers' took place between Sept. 15 and Sept. 23.

(Reporting by David Milliken; Editing by Hugh Lawson)