The number of cases are a slight rise on last Monday when the UK recorded 36,100 positive tests but the number of deaths has fallen compared to a week ago, when 49 covid-related deaths were recorded.
The figures compare with the 32,417 cases and 58 deaths within 28 days of a positive test reported on Sunday.
The Government said the olatest daily figures brings the UK total number of Covid-related deaths to 136,208
Separate figures published by the Office for National Statistics show there have now been 160,000 deaths registered in the UK where Covid-19 was mentioned on the death certificate.
Meanwhile, another 14,120 people have received a first dose of a vaccine, taking the total number of people to have had one jab to 48,736,534.
And a further 24,851 people had their second doses, bringing the number of fully vaccinated people in the UK to 44,764,324.
The UK has joined a handful of countries to have fully vaccinated more than two-thirds of its entire population against Covid-19.
The more than 44.7 million second doses now delivered in the UK is equivalent of just over 66.6% of the total population.
Other countries to have already passed this figure include Canada (with at least 70% of people fully vaccinated), Chile (73%) and Singapore (76%).
A number of European nations have also beaten the UK to the milestone of two-thirds fully jabbed, such as Italy (67%), Belgium (71%), Ireland (73%) and Spain (77%).
Portugal continues to lead the world, however, with at least 84% of its total population having now received two doses of the vaccine.
The latest figures come as families who have lost loved ones to coronavirus are set to meet Boris Johnson in Downing Street, where they will press him to “immediately” begin a public inquiry into his government’s handling of the pandemic.
Members of the COVID-19 Bereaved Families for Justice campaign group will hold talks with the prime minister in Number 10 on Tuesday.