Coronavirus cases in the region have risen quickly in recently weeks, data has shown.
The number of infections in Suffolk rose to 250 in the week up to June 26, up from 150 the week before - an increase of 66%.
Essex has also seen cases go up to 1,227 in the week up to June 26, from 576 the week before.
That is a 113% rise in the county overall, with Tendring seeing an 83.3% rise and Colchester a growth of 86.7%.
The number of people in hospital with coronavirus remains low, however.
East Suffolk and North Essex NHS Foundation Trust (ESNEFT) - which runs Ipswich and Colchester hospitals - recorded just seven Covid patients as of Tuesday, June 29.
West Suffolk Hospital NHS Foundation Trust had just one patient, and there have been no coronavirus-related deaths in Suffolk since June 2.
However, public health director at Essex County Council, Dr Mike Gogarty, warned that rates "are higher than what we are seeing" as vaccinated people - who may be asymptomatic carriers of the virus - mix with unvaccinated young adults.
Essex saw four coronavirus-related deaths in June.
"It's rising really quickly," Dr Gogarty said of the Covid infection rate.
"It's most important to get vaccinated as soon as possible.
"People should really be tested regularly."
He also warned that people will still get infected after July 19, when most coronavirus restrictions are due to be lifted.
Dr Gogarty warned people aged 60 to 80 who had not been vaccinated were most at risk.
He said reports of a possible third wave are "a concern" - but highlighted that the vaccine is working against the highly infectious Delta variant, first found in India.
Nick Hulme, chief executive of ESNEFT, said: “Now more than ever it’s important to not become complacent.
"Anyone who gets Covid-19 can become seriously ill or have long-term effects."
Stuart Keeble, director of public health for Suffolk, said the "worrying increase in Coronavirus" is expected to continue but rates are "considerably lower" than in other parts of the country.
Mr Keeble added: “We know from our experience of this hard fought 18 months that these measures keep us all safe. Please stick with it Suffolk.
“Even with two jabs you can still catch the virus, albeit with less-severe consequences, but it can still make you feel very poorly and you risk spreading it to someone who hasn’t been vaccinated yet. Everyone must continue to live within the guidelines.”
Ipswich MP Tom Hunt said he supported prime minister Boris Johnson's delay to lifting Covid restrictions until July 19.
However, he said new health secretary Sajid Javid had made him feel "confident" that the easing of lockdown would go ahead, bringing a much-needed boost to businesses forced to close for months.
"The link between cases, hospitalisation and deaths have been severed," Mr Hunt said.
"To what extent is the number of cases the key thing.
"We can have cases as high as possible if there is no pressure on the NHS and no increase in fatalities.
"But it's better to have a low number of cases."
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