Dame Jenny Harries told BBC Radio 4’s Today programme there were three million people with Covid in the week to March 25 – “a very high level”.
“But what we’re not seeing of course is a significant translation of that into serious illness, hospitalisations and most importantly, deaths.
“There has been a small uptick in deaths in the last week and again… some hospitals are coming under significant pressure and we shouldn’t underestimate that.
“But overall, immune defences through the vaccination programme has been really successful and of course we now have treatments.”
Meanwhile, Dr Layla McCay, director of policy at NHS Confederation said “now is really not the time for complacency”.
She said that cases and hospital admissions continue to be high, with an estimated 4.26 million cases reported last week and more than 15,000 people currently in hospital with the virus, similar to the numbers seen in mid-January.
“At such high levels there is a real risk that a significant number of people become so unwell they will need to be admitted to hospital,” she said.
“While the success of the vaccine and new Covid treatments, offer real hope as we learn to live with the virus, we really do still need to be cautious as the threat from this disease has not disappeared entirely.
“There is much which is still uncertain, including our long-term immunity and the emergence of future strains and a solid testing infrastructure and clear guidance from the Government will continue to be crucial.”
It comes as the Government gets set to ditch free Covid tests for most people from Friday in England.
Also from Friday, as part of the Living with Covid strategy, venues and events will be advised against using the NHS Covid pass.
Latest Office for National Statistics (ONS) figures show around one in 16 people in private households in England – or 3.5 million people – are likely to have had Covid in the week to March 19.
This is up from one in 20, or 2.7 million people, in the previous week. New statistics come out each week on a Friday.
Asked if it is the right time to end free Covid testing, Dame Jenny said the UK must come to terms with the pandemic remaining unpredictable.
She said: “The pandemic takes its own course and it will remain unpredictable to a large extent for the next say 18 months to two years, I think is general consensus, and we will have to be continuously be alert to monitor those rates and to respond appropriately to any new variants.
“But as with other respiratory viruses such as flu… at some point we have to come to terms with that”.
She urged people to take precautions such as mask-wearing in shops and on public transport.
The move to end free mass testing has been met with criticism from a range of groups.
Professor Devi Sridhar, chairman of global public health at the University of Edinburgh, said the end of free mass testing was “a major mistake”.
Scrapping free testing at a time when infection levels were “eye-wateringly high” was a “premature move”, she said, especially when it has been the key to keeping society open and without further restrictions.
Meanwhile, Professor Stephen Reicher warned taking away free mass testing to save money could actually end up costing “tens of billions of pounds” in the long-run.