The number of new Covid cases recorded in England each day jumped by 62% - more than 10,000 cases - in the first week of October compared to the week before.
Office for National Statistics (ONS) data shows there were an average of 27,900 new cases per day of Covid-19 in private households in England between October 2 and 8.
The estimated number of confirmed cases is at its highest level in around five months, with cases rising rapidly.
That's 10,700 more cases recorded each day compared to the average from the week earlier, when an estimated 17,200 new cases per day were recorded from September 25 to October 1.
Figures from the Covid-19 infection survey showed the number of infections has "continued to increase rapidly in recent weeks" - with the highest rates of positive tests among older teenagers and young adults.
But the ONS said there are now also more signs of growth in the age groups covering 25 to 69-year-olds.
The ONS bases the measure on analysis of more than 450,000 swabs over the past six weeks from the public - regardless of whether they have symptoms, or not.
Ruth Studley, Head of Analysis for survey, said: "Our latest data shows infections continue to rise, with more than a third of a million people estimated to be infected."
She added it is "the highest levels we have seen since the survey began in May."
The ONS said cases were rising "rapidly," with an estimated 336,500 people having coronavirus in the week to October 8 - the equivalent of around one in 160 people.
How do the figures compare regionally?
Geographically, there continues to be clear evidence of variation in Covid infection rates across the regions of England, the ONS said.
While the lowest rates are in south-west England, eastern England and south-east England.
Meanwhile, Professor Graham Medley, an expert in infectious disease modelling at the London School of Hygiene and Tropical Medicine and a member of Sage, has said he believes that in terms of healthcare, "some areas are going to be back to the same kind of position they were at the end of March".
What are the other analysts saying?
The Medical Research Council (MRC) biostatistics unit at Cambridge University published new predictions on Monday on how fast the epidemic is growing across the country.
It said around 47,000 Covid-19 infections are occurring daily across England - with deaths expected to hit 240 to 690 per day by October 26.
The Cambridge University researchers estimated cases are doubling in under seven days, with a "substantial proportion" of those being asymptomatic.
The latest government figures showed 18,980 lab-confirmed new coronavirus cases as of 9am on Thursday, while a further 138 deaths were reported. But experts say lab-confirmed cases do not represent the true scale of the outbreak.
Separate figures from the Covid Symptom Study UK Infection Survey suggest there were 27,762 daily new symptomatic cases of Covid-19 in the UK on average over the two weeks up to October 11.
This is up from 21,903 the week before.
Researchers behind the study used regional data to suggest which places could face tier 3 restrictions next.
Burnley and Manchester come top of the list followed by Newcastle upon Tyne, Nottingham, Bury, Hartlepool, Salford, Sheffield and Leeds.