Boris Johnson is expected to announce on Tuesday if the hospitality sector can reopen on 4 July, and that the 2m distancing rule in England will be relaxed, with some conditions.
Non-essential shops have reopened in England already, with retail resuming in Wales from today.
Health Secretary Matt Hancock has said England is "clearly on track" to further ease lockdown restrictions.
But No 10 warned the moves would be reversed if they led to a virus surge.
The PM discussed England's approach to the changes with the Covid-19 Strategy Committee on Monday, ahead of an announcement in Parliament on Tuesday.
Mr Johnson is also expected to announce a reduction in the 2m social distancing rule to 1m, with some mitigating measures.
The change to the rule, which follows a government review, is expected to come into effect on 4 July.
Ministers are also expected to bring forward legislation this week aiming to help businesses cope with social distancing requirements.
The PM's spokesman said the Business and Planning Bill would help firms "adjust to new ways of working, and help them capitalise on the summer months".
Labour MPs have called for ministers to be transparent on the findings of the 2m rule review.
Shadow health secretary Jon Ashworth has said the party's support would depend on mitigations being introduced on face-shielding, and testing and tracing.
Science 'has evolved'
Earlier Security Minister James Brokenshire said the 2m rule review would be informed by scientific evidence but also "experience around the world as well".
He told BBC Breakfast it was also important to recognise the importance of other factors on safety, such as whether people are indoors or outside, or whether they are wearing face coverings.
He added that the review would also take into account the latest understanding of how the virus is transmitted, which "has evolved over the last number of weeks".
Mr Hancock has suggested that customers may have to register when entering pubs and bars so they can easily be traced if they come into contact with a coronavirus case.
Asked on Sunday about plans for registration and ordering drinks through smartphone apps, he said: "I wouldn't rule it out. It isn't a decision we've taken yet, but there are other countries in the world that take that approach."
He added that he "very much hoped" the 2m rule can be lowered, with "mitigations" to cut the risk of transmission.
The government has come under pressure from the hospitality sector to lower the rule, with many saying it would be impossible to trade under the current restrictions.
2m or not 2m?
Some Tory MPs and members of the hospitality sector have been appealing to the government to lower the 2m rule to 1m, as many venues say they would be unable to open otherwise.
The World Health Organization recommends a distance of at least 1m (just over 3ft), but the UK government's scientific advisers say that distance carries up to 10 times the risk of being 2m apart.
The other nations of the UK are yet to announce any plans to change the 2m distance rule.
Scottish First Minister Nicola Sturgeon has asked scientific advisors to review the circumstances in which it might be reduced alongside "additional mitigations".
In Northern Ireland, where hotels, bars, restaurants and cafes are set to reopen from 3 July, Economy Minister Diane Dodds has said she is open to changing it.
A change has also not been ruled out in Wales - where First Minister Mark Drakeford said he would support a reduction if Welsh advisers said it was safe.
In his speech on Tuesday, the PM is expected to warn the public they must continue to follow social distancing guidelines to "keep the coronavirus under control".
He will also reiterate pledges to use the NHS Test and Trace system to detect and control local outbreaks through "targeted lockdowns".
A No 10 spokesman said: "The reason we are able to move forward this week is because the vast majority of people have taken steps to contain the virus.
"The more we open up, the more important it is that everyone follows the social distancing rules.
"We will not hesitate to put the handbrake on to stop the virus running out of control."