The prime minister’s official spokesman said guidance will be given to councils but that events would be allowed as long as social distancing was maintained.
There will be a national service at the Cenotaph in London that will be broadcast on TV.
“We are certainly not cancelling Remembrance Sunday events but we must be mindful of the risks such events pose, especially to veterans who are often elderly,” the spokesman said.
“What we are saying to local authorities in England is that they may organise remembrance services but they should be outside and social distance should be maintained.
“We will be updating the guidance shortly.”
The spokesman added: “It’s important that the country can continue to come together to remember the sacrifice of those who have died in the service of their country, and we will ensure that Remembrance Sunday is appropriately commemorated while protecting public health.”
The National Service of Remembrance at the Cenotaph in London is held on the closest Sunday to 11 November and marks the contribution of British and Commonwealth military and civilian servicemen and women in the two world wars and later conflicts.
The service is attended by senior members of the Royal Family, including the Queen, and members of the government who pay their respects in the traditional wreath-laying service.
The annual march past the Cenotaph will not take place, but some veterans will be invited to attend the service, which will be made COVID-secure by minimising attendance and ensuring strict social distancing measures are in place.
In a statement released in October, the Department for Digital, Culture, Media & Sport urged the public to stay at home and remember the fallen for the national moment of silence at 11am as the service is broadcast nationwide.
The march past the Cenotaph on Whitehall normally consists of 10,000 military veterans and bereaved family members.
The British Legion said of its cancellation: “Owing to the COVID-19 pandemic and in light of the risks posed, the annual Remembrance Sunday March Past the Cenotaph will not take place this year.
“We recognise this will be deeply disappointing for all who were due to take part and it is not a step that has been taken lightly.
“This decision has been taken by the government based on expert advice to protect the health and well-being of those who would have been travelling to and participating in the event.”
On Saturday, Boris Johnson confirmed that England would return to a full national lockdown from Thursday.
Pubs, restaurants and non-essential shops will be forced to close, curbs on travel will be imposed, households will be banned from mixing inside homes and church services will be cancelled.
The prime minister said the rules will be reviewed on 2 December.
Watch: The importance of the Remembrance Day in Commonwealth nations