Casinos and bowling alleys will remain shut, with Boris Johnson saying it was time to "squeeze the brake pedal", the BBC reported.
Wedding receptions of up to 30 people were meant to be allowed as part of the changes but cannot yet happen.
Face coverings will be mandatory in more indoor settings, such as cinemas.
People attending places of worship will also be required to wear face coverings, in a change that will be applied from next weekend.
But planned changes to guidance for those who have been shielding during the pandemic, and advice for employers, will still go ahead.
Johnson made the comments during a special Downing Street briefing, where he was joined by England's chief medical officer, Prof Chris Whitty.
Prof Whitty warned that it might not be possible to ease the lockdown any further, explaining that the "idea that we can open up everything and keep the virus under control" is wrong.
Asked whether it was safe for England's schools to open fully to all pupils in the autumn, he said it was a "difficult balancing act" but "we have probably reached or neared the limits of what we can do in terms of opening up society".
The rethink follows new restrictions for people in parts of northern England, after a spike in virus cases.
The prime minister said progress against coronavirus continues, with the daily and weekly number of deaths falling, but warned that some European countries are "struggling" to control it. The UK must be ready to "react", he said.
A further 120 people have died with the virus in the UK, according to the latest figures, and 880 new cases have been recorded.
Highlighting the latest figures from the Office for National Statistics (ONS), Johnson added: "The prevalence of the virus in the community, in England, is likely to be rising for the first time since May."
He said that the reopening of society had always been "conditional" on "continued progress against the virus", but with "numbers creeping up" it was time to "squeeze that brake pedal in order to keep the virus under control".
He urged people to "follow the rules, wash our hands, cover our faces, keep our distance - and get a test if we have symptoms", summing the advice up with a new slogan: "Hands, face, space, get a test".
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