She added the government has introduced legislation to speed the policy up.
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“We want to move as quickly as possible to relocate people from the UK to Rwanda,” she said.
In March, a government source told Sky News that UK officials were working towards the first flights to Rwanda leaving “by the summer” after Ms Braverman signed an update to the agreement with Kigali.
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It expanded the scope of the legislation to “all categories of people who pass through safe countries and make illegal and dangerous journeys to the UK”.
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2:08
Suella Braverman asked if the Conservatives are failing to deal with migrants crossing the Channel
Ms Braverman has previously described deporting migrants to Rwanda as her “dream”, saying it is her “obsession” to see a plane take off.
Asked about that, she said: “I care very passionately about stopping the boats, just like the prime minister does, just like the vast majority of British people do.”
But when presented with charts showing a steep rise in net migration, asylum seekers in temporary accommodation and the number of people arriving in small boats under the Conservative government, Ms Braverman refused to say their approach is failing.
“I accept we’ve got unsustainable [numbers], I’ve been very clear about the crisis and I’m aware of the numbers,” she said.
The home secretary added that “context is important” and said: “We’re in the middle of a global migration crisis.”
She said it is not just the UK facing “unprecedented numbers of illegal arrivals” but the French, the UK and “other Western democracies”.
“We’re all grappling with unprecedented numbers of people. We have to take action now,” she said.
“That’s why we’ve introduced a bill with tough measures which are both firm and humanitarian.”
Ms Braverman also refused to take responsibility for a spike in asylum seekers being housed in temporary accommodation.
She insisted the situation is being sorted by deporting “about 500” Albanians and signing a deal with the French to enhance cooperation in the Channel.
“And we’re now about to procure and roll out bespoke accommodation for asylum seekers so we can start taking people out of hotels and moving them into more affordable and appropriate accommodation,” she added.