Between 12 and 18 July, a total of 1154.7 infections per 100,000 people were recorded among those aged 20 to 29, according to data from Public Health England (PHE).
This is the highest figure recorded for any age cohort since the beginning of the pandemic, said Dr Yvonne Doyle, medical director at PHE.
“Everyone in this age group should come forward and get their two doses of the vaccine to make sure they have the best chance of being protected,” she said.
Labour’s Jon Ashworth, the shadow health secretary, warned that rising infections among young people would slow down vaccinations, “given you have to wait 28 days after infection for [a] jab”.
The lowest case rates have meanwhile been recorded in those aged 80 and above, with a 7-day rate of 60.6 per 100,000.
The seven-day hospitalisation rate is also continuing to increase for England, the PHE figures show.
Between 12 and 18 July, 5.88 people per 100,000 were admitted to hospital with Covid - up from 4.55 in the previous week. Regionally, admissions were highest in the North East, with a rate of 13.24 per 100,000 population. For age, rates continue to be highest in the over-85s.
Admissions to intensive care units are also rising - up from 0.41 people to 0.51 per 100,000.
Despite efforts of the government to return to normality, Dr Doyle warned that “Covid-19 has not gone away.”
“It is vital we all remain cautious,” she said. “Remember that meeting outside is safer than inside, get two doses of the vaccine as soon as you can, isolate if you are told to by NHS Test and Trace and if you show symptoms stay home and get a PCR test. We all still have a part to play.”
In the week up to 18 July, vaccine coverage in England stood at 62.3 per cent for one dose, while 48.5 per cent of adults had been fully vaccinated. This rises to more than 90 per cent for all cohorts over the age of 65.
The high prevalence in cases among people in their twenties has been attributed to Euro 2020, which saw large numbers of fans travelling to Wembley and gathering together to watch the football.
Earlier this month, one UCL modeller predicted that England’s final two matches of the tournament will have gone on to cause at least a million cases across the country.
Professor Paul Hunter, an expert in health protection and infectious diseases at University of East Anglia, also said that “it is difficult to escape the conclusion that celebrations around the Euros have been an important factor in driving up the epidemic in the UK”.
The rising infection rates come as a record number of people were told to isolate by the NHS Covid-19 app after more than 600,000 alerts were sent to users in a week.
Former health secretary Jeremy Hunt said the government risks "losing social consent" for isolation if it does not immediately bring forward the relaxation of quarantine rules for the fully vaccinated.
Business secretary Kwasi Kwarteng told shoppers not to panic in the face of supermarket shortages and attempted to ease concerns over the rising alerts as Covid-19 cases soar.
He said a "very narrow" list of sectors whose workers will be exempt from isolation rules would be published on Thursday, but Downing Street later suggested it would instead be "examples of the sectors where exemptions could apply".
Warnings of staffing shortages mounted as NHS figures showed 618,903 alerts were sent to users of the coronavirus app in England and Wales in the week to 14 July, telling them they had been in close contact with someone who had tested positive for coronavirus.