Matt Hancock has acknowledged that there are "operational challenges" in the testing system as he was summoned to answer an urgent question on the situation in the Commons.
The Health Secretary told MPs it might be "a matter of weeks" before the problems are resolved after widespread complaints that tests are unavailable, people are waiting more than 24 hours for results, or are being forced to travel long distances to get a test.
Last week a union said County Durham teachers are being forced to travel hundreds of miles for coronavirus tests.
NEU Durham secretary Emma Parker said staff were facing trips to Cumbria and as far as Barnsley to have tests carried out due to a lack of availability in the area.
But Mr Hancock told MPs that the average distance travelled to a test site is now 5.8 miles, down from 6.4 miles last week.
He told the Commons on Tuesday: "Everyone in this House knows that we're doing more testing per head of population than almost any other major nation, and I can update the House that we have now carried out over 20 million tests for coronavirus in this country.
"As we expand capacity further, we're working around the clock to make sure everyone who needs a test can get a test."
We want to know your views on the current testing system. Is it up to scratch or do you think there is a better way?
Have you tried to book a test locally? Have you been directed miles away from home to get one? Let us know in the survey below. Click here if the form doesn't load.
