The prime minister says there is a "growing consensus" that Britain is descending into lawlessness.
The government department has seen four different home secretaries in five years.
The deputy prime minister said his former cabinet colleague did not need to apologise.
The former home secretary's latest outburst came in the wake of the Commons Gaza vote chaos.
Taxpayers are facing a £290m bill for the controversial policy.
The BBC presenter said the former home secretary was "a headline-grabber".
Immigration minister's resignation leaves prime minister's flagship deportation policy in tatters.
In a direct challenge to Rishi Sunak, the former home secretary warned the party will "die" if a new immigration law is too weak.
And he still doesn't know when the first migrants will be deported to the east African country.
Plan labelled "cruel" by critics – but former home secretary says the government can "go further".