A member of Labour’s frontbench has suggested the head of the ailing NHS Test and Trace system should be sacked.
The prime minister acknowledged failings in the multi-million programme last week and said he wanted to see improvements.
But Northern Ireland Secretary Brandon Lewis defended Baroness Harding saying she has done a "very good job".
He rejected a call by Tory MP Sir Bernard Jenkin for a senior military commander to take charge instead.
"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," Mr Lewis told Sky News's Sophy Ridge on Sunday programme.
Dr Allin-Khan said Baroness Harding's position was "untenable".
"The huge take-home message here is ... the Tories can see just how catastrophic the Test, Trace and Isolate system has been," she said.
"It's time to put it back to the local communities who know their communities best.
"(Baroness Harding's) position is very difficult, it's untenable really, but fundamentally this comes down to the responsibility of the Government, they have failed people.
"There are people going into this Christmas period not knowing if they're going to be able to hug their elderly parent in a care home for the last time or not.
"We need to be speaking up for them and for that we need to put it back into the hands of our local public health teams."