People being unable to secure Covid tests or being asked to travel hundreds of miles for one are a result of public confidence in the test and trace system and a resulting increase in demand, Boris Johnson has argued at a prime minister’s questions.

With Keir Starmer ignoring the furore over the government’s admission it could break international law in seeking to renege on some of the Brexit withdrawal agreement, the Labour leader instead used all of his questions to focus on what he termed a lack of government competence over testing.

In response, Johnson continued his recent pattern of ignoring the substance of Starmer’s questions, to accuse him of “carping” and undermining public faith in the testing system.

The closest the prime minister came to responding to Starmer’s repeated queries on the reasons for people not being able to access tests was to say it was down to increased demand, and to indicate some of this was due to people without symptoms seeking tests.

“The issue at the moment is that there has been a massive increase in the number of people who need or want tests, particularly people who don’t have symptoms,” he said. “And we need to prioritise people such as NHS frontline staff, our care workers, who urgently need those tests.”

Responding to another question, Johnson said: “It’s obviously a function of the growing demand and the growing public confidence in NHS test and trace that we have to supply more and more tests.”

But Starmer received no direct answers to a series of queries, including on whether a lack of laboratory capacity was to blame, and what was being done to address the issue.

Instead, Johnson praised what he called the “heroic” efforts of testing staff, and said Starmer’s questions were an “attempt to undermine confidence in test and trace”.

The Labour leader responded by accusing Johnson of failing to properly engage. He said: “Nobody is attacking here. The prime minister needs to know how anxious hundreds of families are. In the last few weeks they’ve been sent all over the country or been told there are no tests. It can’t be brushed off.”

On another occasion, he replied: “What’s undermining confidence is families being told to go hundreds of miles and they can’t get a test. I just want it fixed. I don’t need to have an argument; accept there’s a problem, tell us what the solution is, so we can all muck in and try to make it better, and tell our constituents. Is he saying there are too many people coming forward for tests, a capacity problem, or not?”

Johnson did say he took responsibility for any failings, “as I have done throughout for the entire handling of the coronavirus crisis”, but did not engage with any of Starmer’s questions, such as why some families in London had been told either they could not get a test, or to travel to places such as Swansea and Inverness. Instead he said the Labour leader should be more supportive.