Last week, testing expanded to all key workers in England and their households.
Now, all care home residents and staff, people over 65 and those who must leave home to work are entitled to a test.
With just over 43,000 taking place as of Monday, No 10 aims to hit its target of 100,000 tests per day by Thursday.
The expansion in eligibility means 25 million people can now book through the government's test-booking website, testing coordinator Prof John Newton told BBC Radio 4's Today programme.