The Government is resisting pressure to sack the head of NHS Test and Trace amid deepening concern among ministers and MPs that the system is failing to stem the spread of coronavirus.

Northern Ireland Secretary Brandon Lewis insisted that Baroness Harding was doing “a very good job” after one senior Conservative MP called for her to be replaced by a senior military commander.

However, Labour warned her position was “untenable” as it emerged ministers were considering cutting the time people have to self-isolate if they have been in contact with someone who has the disease because of concerns over public compliance.

At the same time it was reported that Boris Johnson has become “disillusioned” with the data he is receiving from Test and Trace after some of the figures he was given turned out to be inaccurate.

During a round of broadcast interviews, Mr Lewis rejected calls for Lady (Dido) Harding – who is a Conservative peer – to be dismissed, although he acknowledged that the service needed to improve.

“What Dido has done is put together and drive forward a team that has come on so much in the last few months,” he told Sky News’s Sophy Ridge on Sunday programme.

“We want to see it improve, we want to see it grow and get better and better. That’s how we fight this virus. But actually I think Dido and the team have done a very good job to get to where we are.”

However, in a scathing attack, senior Tory backbencher Sir Bernard Jenkin said there was a “vacuum of leadership” at the top of the organisation and that public consent and co-operation was “breaking down”.

The immediate priority is to fill the vacuum of leadership in Test and Trace, which is destroying cooperation and compliance

Writing in The Sunday Telegraph, he said Lady Harding should be given a “well-earned break” so she and others could “reflect on the lessons learned so far” and that a senior military figure should be appointed in her place.

“There is a spaghetti of command and control at the top, which is incapable of coherent analysis, assessment, planning and delivery,” he wrote.

“The immediate priority is to fill the vacuum of leadership in Test and Trace, which is destroying cooperation and compliance.

“Government harnessed the military to regain control in the foot and mouth crisis; the Prime Minister should follow that example today, by installing a single leader, a three or four star military commander with a reputation for handling complexity under stress.”

Appearing on the Sophy Ridge on Sunday programme, Sir Bernard, who chairs the Liaison Committee of senior MPs which questions the Prime Minister twice a year, insisted his comments about Lady Harding had been meant “kindly” and that she was a “tremendous asset”.

However, he added: “The Test and Trace capability clearly needs to move up several gears and it’s what leadership does, not who leadership is that really matters. It is the sense that there is a lack of an overall strategy which I think is at the heart of the problem.”

The row comes after the Test and Trace system last week hit a record low with just 59.6% of the contacts of people who tested positive for the disease being successfully contacted and told to self-isolate.

For Labour, shadow mental health minister Rosena Allin-Khan said Lady Harding’s position had become “untenable”.

“The Tories are in-fighting because even they can see just how catastrophic the test, trace and isolate system has been,” she told the Sophy Ridge on Sunday programme.

Meanwhile, Mr Lewis confirmed officials were looking at reducing the time people contacted by the Test and Trace system would be required to quarantine at home from 14 days to between 10 days and a week.

Government sources acknowledged the move reflected concerns people were failing to respond when they were contacted by the system because of fears they could face a lengthy period of self-isolation.

Mr Lewis said: “We want to make sure we are moving with science and allow people to live and work within this virus as best as we can while always making sure we protect people’s health and the NHS.”

Meanwhile, the head of the Office for National Statistics, Professor Sir Ian Diamond, warned it was too early to say the spread of the disease was slowing, despite some signs in the latest data.

“I am extremely nervous about taking just initial data and pushing things forward, and say ‘it’s fine’,” he told BBC One’s The Andrew Marr Show.

“We might see the rate of increase slow a little as we get further data over the next few weeks, but we’re still at a relatively high level. What we really need to do is to bring that level down.

“Even if we were to get R in the North to around about 1, it would continue to have infections at a high rate. I really do think it’s too early to say on slowing down.”