Toolmaking is one of the areas where skill shortages are reported by recruitment trade body REC. Photograph: DPA Picture Alliance/Alamy Stock Photo

Fresh evidence of skills shortages has fanned fears about British companies’ long-term prospects if the government follows through on talk of an immigration crackdown.

A monthly check on the recruitment market published on Friday added to signs that employers have rebounded from the initial shock of the Brexit vote at least for now. Permanent hiring rose for the second month running in September, after declining in June and July.

But the Recruitment and Employment Confederation (REC) also found the availability of permanent and temporary staff continued to fall in September. At the same time demand for staff continued to rise and there was solid growth in starting salaries for people placed in permanent jobs.

The trade body said that based on its poll of 400 recruitment consultancies, those jobs suffering skills shortages included accountants, HGV drivers, architects, care workers, scientists and toolmakers. For temporary jobs there were shortages of electricians, call centre staff and bricklayers.

Theresa May hinted at a tougher line on immigration in her speech to the Conservative party conference this week and home secretary Amber Rudd incited a backlash from business leaders over proposals to force companies to disclose how many foreign workers they employ.

REC policy director Tom Hadley said the government must be mindful that many UK employers were already facing talent shortages.

“Despite some of the rhetoric at this week’s Conservative party conference, we will continue to need workers from overseas in a range of sectors from engineering to healthcare,” he said.

“The business community must have a role in developing an immigration model that strikes the right balance.”

The report, compiled for REC by data company IHS Markit, showed that as demand for staff rose and skills shortages continued to be felt, successful job candidates were able to secure higher starting salaries last month.

Companies’ apparent willingness to continue hiring despite worries over Brexit chimes with other recent indicators suggesting business activity and confidence has rebounded.

UK business confidence recovered to be almost at pre-referendum levels during September driven by large increases in organisations’ optimism for both the UK economy and their own prospects over the coming year, according to a poll from YouGov released on Friday.

For first time since the referendum, more than half of businesses were optimistic about their prospects in the next year, according to YouGov’s report, which was compiled with the Centre for Economics and Business Research (CEBR) using responses from 500 business people.

The report’s main business confidence index rose to 112.4 last month, not far off June’s reading of 112.6 and May’s 112.5.

“It is now clear that business confidence took a short-term stumble in the wake of the EU vote instead of a long-term fall,” said Scott Corfe, director at the CEBR.

“However, it should be noted that this research was carried out before the Conservative party conference and all the talk of ‘hard Brexit’ implying that the UK would prioritise immigration restrictions over access to the European single market. Once the shape of our economic relationship with the EU becomes clearer, these figures could shift notably.”