If a migrant travels to Britain from either nation without permission they will not be able to claim asylum under a new draft legislation tabled on Wednesday.
But a campaign group said the government should stop focusing on "unprincipled policies” and try to come up with a fairer, more efficient asylum system.
But since the year started, more than 26,000 migrants have arrived after the dangerous journey, according to the latest UK government figures.
The Illegal Migration Act brought into law the government’s policy of sending some asylum seekers to Rwanda.
Ministers are awaiting a Supreme Court judgment on whether the plan is legal, with no deportation flights yet to take off for the East African nation.
100,000 migrants cross the Channel in five years - in pictures
Home Secretary Suella Braverman, who last week visited the Greek island of Samos to “learn” from the country’s “policy of deterrence” and “tough measures” on migration, said expanding the list “sends a clear message that if you come here illegally, you cannot stay”.
“We remain committed to delivering the measures in our Illegal Migration Act, which will play a part in the fight against illegal migration,” Ms Braverman said.
But Jon Featonby, chief policy analyst at the Refugee Council, said: “Rather than put in place a functioning process, the government is trying to exclude more and more people from the UK’s asylum system.
"Most of the Illegal Migration Act hasn’t even come into force yet, and the government are already trying to make it even more draconian.
“Instead of evermore unworkable and unprincipled policies, the government should be focusing on running an asylum system that gives people a fair hearing in the UK, making decisions in months not years.”