It is the first time the UK government has issued the advice, but the Scottish government already recommends masks.
People are also allowed to meet one person from another household outside.
It comes as Boris Johnson announced on Sunday a “conditional plan” to begin lifting England’s coronavirus lockdown. Scotland, Wales and Northern Ireland have their own powers over the lockdown and have not lifted measures to the same extent.
Mr Johnson will speak to Parliament at 15:30 BST on Monday. He will then lead the government’s daily Downing Street press briefing which, due to the Commons statement, has been moved to 19:00.
“As more people return to work, there will be more movement outside people’s immediate household,” the guidance says.
“This increased mobility means the government is now advising that people should aim to wear a face covering in enclosed spaces where social distancing is not always possible and they come into contact with others that they do not normally meet, for example on public transport or in some shops.”
Other countries have already introduced rules about wearing face masks. Advice in Wales and Northern Ireland has not changed and face coverings have not yet been recommended for the general public.
The document – called “Our Plan to Rebuild: The UK government’s Covid-19 recovery strategy” – says homemade cloth face coverings can help reduce the risk of transmission in some circumstances.
They don’t protect the wearer but protect “against inadvertent transmission of the disease to others if you have it asymptomatically”, the guidance says.
And it adds a face covering is not the same as face masks, such as those worn by healthcare workers which “must continue to be reserved for those who need it”.
From Wednesday, people in England will also be allowed to meet one person from outside their household as long as they stay outdoors and stay 2m apart, the advice says.
Sage, the government’s group of scientific advisers, say the risk of infection outside is significantly lower than inside, according to the document.
As the prime minister set out on Sunday evening, the guidance also sets out the government’s three-step plan.
In step one, starting on Wednesday 13 May, workers who cannot work from home should travel to work if their workplace is open. The government is also urging more vulnerable children to attend school if they are able to
In step two, which will begin no earlier than 1 June, nurseries and primary schools will begin a phased return beginning with early years, reception, and years one and six. Some businesses will be able to reopen and sporting events will be able to take place behind closed doors
In step three, which will start no earlier than 4 July, more businesses will be able to open – although some, which are crowded by design, will not be able to open. The aim is to reopen businesses such as hairdressers and beauty salons
All dates could be delayed if not enough progress is made in tackling the virus – and restrictions could be reintroduced, the guidance says.
The guidance also said the government’s ambition is for all primary school children in England to return to school for a month before the summer.
It is likely that the government will continue to advise people who are clinically extremely vulnerable to continue to shield beyond June, the document adds.