Ministers have attempted to clarify the rules around Boris Johnson’s lockdown, amid confusion over who is allowed to travel to work, whether children can visit separated parents and what counts as exercise. Michael Gove, the Cabinet Office minister, gave more guidance on Tuesday morning on the unprecedented restrictions announced by the prime minister, which will be enforced by police. Under the rules, people must stay at home unless they have to leave the house to work, to get essential supplies of food or medicine, to help the vulnerable or for one period of exercise a day. The biggest confusion was over whether workers should count their jobs as essential, with construction workers, taxi drivers and tradespeople unsure. Some retail workers, such as staff at Sports Direct, were still called into their jobs by employers despite the order for non-essential retail to close. Sports Direct later changed its mind and said it was closing its stores. Gove said construction workers should still be going to work while staying two metres apart and tradespeople, such as plumbers and electricians, could attend emergencies in people’s homes. He said it was “unhelpful” and “wrong” for stores such as Sports Direct to remain open to sell sports and leisure wear, arguing that people generally had the appropriate clothing to go for a run or walk already. Non-essential shopping deliveries – such as clothes and toys – would be allowed to continue. Gove issued a series of stark warnings about the consequences of flouting the ban. Shown pictures on Sky News of construction workers gathering close together, he said: “Unless you stay at home, then the people you love most may die.” He said help for self-employed people would be outlined “later” by Rishi Sunak, the chancellor, because many of them were still packing on to public transport on Tuesday in the absence of financial support to compensate them for loss of their work. There was also confusion over the movement of children of divorced and separated parents, after contact between households was banned. Gove initially suggested contact would not be allowed but he later corrected himself, saying children under 18 would be permitted to move between the households of their separated parents. On different types of exercise, he said people would be allowed to run, walk or go to an allotment, but not to do more social activities, such as playing golf. Asked why Johnson had changed his mind and introduced more draconian restrictions, Gove told the BBC’s Today programme: “We are living in unprecedented times. All of us recognise this is a land of liberty but we are living in a national emergency.” Labour broadly welcomed the lockdown but some opposition politicians suggested it should go further. Sadiq Khan, the London mayor, said there had been a difference of opinion between him and the government, with City Hall pushing for construction sites to shut down. Rebecca Long-Bailey, the Labour leadership candidate and shadow business secretary, said people should not just be allowed to “order nice things online” that were not essential. “There needs to be a tightly defined list of essential workplaces,” she told the Today programme. She also highlighted the uncertainty faced by self-employed people, who do not get the same 80% of salary support as the employed.