The Prime Minister said he was “determined” to ensure the migrant deportation scheme started within the next few months.
Under the plan, migrants who cross the Channel in small boats could be sent to Rwanda rather than being allowed to seek asylum in the UK.
But peers could frustrate that ambition with Downing Street likely to face attempts to introduce amendments to the legislation.
And former Scottish Tory leader Baroness Ruth Davidson cast doubt that the policy will ever see asylum seekers deported to east Africa.
She told BBC Radio 4 there “are dogs in the street that know” deportation flights are “probably never going to happen”.
However, the PM said: “The Lords will be able to see this is part of the strong majority in the Commons, they can see this is a national priority.”
“And I would urge them strongly to crack on with it because we all just want to get this done. To solve this problem we need to have a deterrent, so when people come here illegally they will be removed.”
Mr Sunak played down the prospect of having to pack the Lords with Tories to get the legislation through. And he added the country was fed up with the “merry-go-round” on the issue.
