Professor Jonathan Van-Tam said the Midlands, Scotland and Northern Ireland are among the areas "burning quite hot" with the virus.
"Look, this is all going very well, but there are some worry signs that people are relaxing, taking their foot off the brake at exactly the wrong time," he said during a government coronavirus briefing.
Some 19 million people in the UK have received their first dose of a Covid-19 vaccine, according to government data published on Friday.
However, British health chiefs fear that the success of the jab rollout, combined with good weather and the UK's recently-announced lockdown exit plan, could cause a dip in public adherence to health measures.
On Friday Mike Ryan, the emergencies chief at the World Health Organization (WHO), also cautioned against people starting to relax their attitudes towards epidemiological protections.
"This is not over, it's not over for anybody, and any relaxation of our resolve is dangerous and we need to be very aware this virus still has a lot of energy," he told a WHO coronavirus briefing.
The UK reported 8,523 new Covid-19 cases on Friday, and a further 345 deaths from the virus within 28 days of positive test.