There were on average 13 positive cases for every 10,000 people, with an overall reproduction number, or R rate, of 0.57 - lower than previously reported.
A blocked nose was the second most common symptom among those who reported any symptoms in the week before testing positive, affecting just over half.
Diarrhoea affected exactly one third of those who experienced any symptoms, while loss of smell and taste affected 30 per cent and 28 per cent respectively.
Fever affected only one in five (20 per cent) who reported symptoms and a new persistent cough 23 per cent.
For the first months of the crisis, these alone comprised the two official symptoms recognised by the NHS.
The report provides an insight into who was infected with the virus between May 1 and June 1, comparing geography, age, sex, ethnicity, key worker status and symptoms.
Beyond the diminished rate of infection, the research found young adults aged 18 to 24 were more likely to test positive than other age groups.
The study comes as experts at King's College London call for skin rashes to be added to the list. They also said that itchy fingers and toes should prompt people to get a test.
It follows separate research from their Covid Symptom Study app, which has 336,000 regular UK users and which found that 8.8 per cent of people testing positive have experienced a skin rash as part of their symptoms.
"This study strongly supports the inclusion of skin rashes in the list of suspicious Covid-19 symptoms. Although it is less prevalent than fever, it is more specific of Covid-19 and lasts longer
"An increased awareness from the public and healthcare professionals regarding Covid-19 skin changes will allow more efficient identification of new and earlier clusters of the disease."
