The PM is expected to announce the next steps on social distancing, face coverings and working from home, as well as on care home visits, during a No 10 news conference later.
Step four of the roadmap was delayed last month to no earlier than 19 July.
Mr Johnson said as we "learn to live with this virus, we must... exercise judgement when going about our lives".
Labour's shadow health secretary Jonathan Ashworth urged the government to confirm "what level of mortality and cases of long Covid" it considers acceptable.
"Letting cases rise with no action means further pressure on the NHS, more sickness, disruption to education - and risks a new variant emerging with a selection advantage," he warned.
Scotland, Wales and Northern Ireland are in charge of their own coronavirus rules, and the Scottish government has suggested it may retain some basic measures including masks at its next review in August.