Chief scientific adviser Sir Patrick Vallance told a press briefing that data from the Office for National Statistics suggested that an estimated 70,000 people in the UK are infected currently with the virus, and around 6,000 new infections are occuring each day - a figure roughly 50% higher than the latest daily reported positive test figure.
Sir Patrick and CMO Professor Chris Whitty warned that cases were now rising in most parts of the UK and that the COVID-19 pandemic now had the potential to expand 'very fast' - particularly with the arrival of autumn and winter.
The government has yet to announce additional lockdown measures - but Professor Whitty warned that the UK has 'in a bad sense, turned a corner', highlighting the need to 'break unnecessary links between households' alongside measures such as self-isolation for symptomatic people, and hand-washing, social distancing and masks to reduce risk of transmission.
Sir Patrick added that there was a chance that 'some vaccine could be available before the end of 2020' in small amounts for key at-risk groups - and that it was much more likely, but not certain, that one or more vaccines currently in late-stage testing could be available 'in the first half of next year'.
The chief scientific adviser warned that cases of COVID-19 were now rising in all age groups - and that the rise in cases was not simply a reflection of increased testing, because positive tests were rising as a proportion of overall tests.
He told the briefing that the pandemic was now poised to advance quickly: 'At the moment we think the epidemic is doubling every seven days. By mid October if that continues you would end up with something like 50,000 cases per day.'
A rise in cases on that scale would be expected to lead to around 200-plus deaths per day a month later, Sir Patrick warned.
Antibody testing shows that less than 8% of the population have been infected, he warned, meaning that 'the vast majority of us are not protected in any way'.
Professor Whitty said the growing second wave was a 'six-month problem that we have to deal with collectively' - warning that in other EU countries a rise in cases in younger people had already translated into a rise in severe cases in older age groups.
He warned that if the rise was not checked, the key risks were more deaths from COVID-19, the NHS becoming overwhelmed by a huge spike in cases, a reduction in other treatments available and the impact of economic disruption on mental health and wellbeing.
The briefing came as BMA leaders called for greater social distancing measures to avoid a dangerous spike in coronavirus cases.