Business groups and unions have called on ministers to provide urgent clarification over which companies will remain open during the coronavirus lockdown amid widespread confusion across Britain.

The head of the Confederation of British Industry, Carolyn Fairbairn, warned that much greater clarity was needed as “companies did not know whether to stay open or close”. She said she would meet with the business secretary to request better guidance.

The warnings come amid widespread confusion among businesses about how to respond to the coronavirus lockdown after Boris Johnson ordered the closure of “non-essential” shops on Monday to limit the spread of the disease.

In one of the most high-profile examples, Mike Ashley’s Sports Direct retail chain had intended to remain open but was forced to backtrack after a public outcry.

Frances O’Grady, the director general of the TUC, said the government needed to crack down on non-essential companies making staff attend work, telling ministers they needed to directly intervene if employers flouted the rules.

“Companies like Sports Direct shouldn’t be putting their profits before people’s lives. No one in non-essential services should be forced to go to work. And no one should be sacked for following official instructions and staying home,” she said.

It is understood that many business leaders are privately furious with ministers for allowing confusion to fester, while workers have also vented anger over their health being put at risk.

Employees at several call centres run by Capita got in touch with the Guardian to raise concerns that the the company was not taking their safety seriously.

One member of staff at a call centre in Runcorn ran by the outsourcing firm Capita said people were still taking calls for the mobile operator O2 involving retention of customers threatening to quit.

“Part of the building sectioned off for deep clean but employees still expected to work,” they said. “The building is filthy desks are never cleaned cleaners only come in to hoover, advisers are to clean the desks. Sanitiser stations are empty, toilets are dirty.”

They said they were concerned about catching the virus and giving it to family members with underlying health conditions and were too scared to speak out as they could be fired. “The way we are being treated is horrendous,” they added.

Capita said it had increased cleaning at sites, staff were working from home where possible and it had no policy to sack people who complain on social media: “The top priority of Capita at this very difficult time is the wellbeing of our people.”

Rachel Reeves, the Labour chair of the Commons business select committee, said the committee received more than 600 messages from concerned workers, including office-based staff, furniture manufacturers, travel agents, estate agents, law firms and TV engineers.

Writing in a letter to the business secretary, Alok Sharma, she said: “It’s vital the government comes forward with immediate clarification.”

An engineer for Sky TV said that the company was still sending him and colleagues into people’s homes, despite the risk of them spreading the disease. He said that the company suspended visits on Tuesday but later told workers they would still make visits to do home moves, installations and servicing.

“I didn’t visit my own mum on mother’s day, yet we are being told to go into the homes of other people’s mothers and grandmothers,” the engineer said.

A spokesperson for Sky said it was taking steps to protect staff, who have been designated as key workers, as well as customers. They said engineers could also refuse a visit if they did not feel safe.

A worker at a BT office in Glasgow said the firm’s call centre could “hold more people than a nightclub” with roughly 350 workers on one floor, but that no social distancing plan was in action.

“The company are telling us they are following government guideline which they clearly are not. Alarmingly they are offering an incentive of an extra £5 per hour for people doing overtime in these crowded, non-essential centres,” he added.

BT said measures were in place to protect staff and workers were providing a vital service to people who needed to communicate during the crisis.

Affinity, a trade union representing TSB employees, said staff at the bank’s Sunderland call centre were worried by a lack of action after two workers’ family members contracted Covid-19.

“Instead of closing the site and instigating a deep clean, TSB has done nothing,” Affinity said. “Staff who raised their concerns have been ignored and been told to carry on as if nothing had happened. That’s unacceptable”

TSB said it followed government guidelines, had told non-key staff to work from home and that those in the office had been spread out.

Construction workers have also continued on site at some projects. Housebuilders Berkeley and Crest Nicholson and the construction firm Balfour Beatty said they were keeping sites open, while Redrow bowed to public pressure to close.

A spokesperson for Berkeley said measures to reduce risks were being taken: “The government has confirmed that home building sites can continue to operate while implementing social distancing guidance.”

Additional reporting by Kalyeena Makortoff and Julia Kollewe