Suella Braverman has been unable to confirm that the first promised deportation flights to Rwanda will take off this summer, as the controversial policy continues to face scrutiny in the courts. The home secretary, whose officials briefed that plans were on track during her trip to the African country last month, played down the prospect of the flights going ahead shortly. “We are making very steady progress,” she told Sky’s Sophy Ridge on Sunday. “I am not going to give a deadline as to when flights will take off.” There remain some legal obstacles to the government’s implementation of its deal to detain and swiftly remove all people arriving by irregular means, with challenges going through the courts. However, a Home Office source had told reporters that “we are certainly working towards getting the flights off before the summer”. Several news organisations interpreted that as a pledge to remove people under the scheme. Braverman was also unable to say when the government’s plan to “stop the boats” bringing people across the Channel would be delivered. “I’m not going to put dates on it, but the rules are clear: if you arrive here illegally, you’ll be detained,” she said. The shadow levelling up secretary, Lisa Nandy, said government strategies to tackle irregular immigration had failed and added millions of pounds to the costs of improving the asylum system – and that Braverman should take responsibility. “She complains about an asylum system that’s broken. I think she really does need to ask who broke it, and the answer to that lies by looking in a mirror,” she told the BBC’s Sunday with Laura Kuenssberg programme. “I think this is a con trick being perpetrated on the British people. The government is not processing asylum claims. They’ve got an enormous backlog. “They’ve added £500m to the costs because of these delays that have been caused by them pursuing all these new strategies: barges that don’t exist, claims to send people to Rwanda that haven’t materialised. What we need is a government that gets a grip on the system.” Braverman refused to confirm reports that ministers were close to signing a contract with Portland port authorities over floating accommodation for refugees, saying she was looking at “all sorts of land and sites and vessels” for accommodation. However, one source confirmed to the Guardian that the Bibby Stockholm, a vessel moored off the Dorset coast, would be used by the government to house refugees from June. The home secretary said: “We’re aiming to roll out these sites very quickly and start making them fit for accommodation purposes and relocate people on to those sites for asylum purposes. “But we’re looking at all options. We’re looking at all sorts of land and sites and vessels and we’re in negotiations with a high number of operators around the country.” Braverman also refused to say whether she still wanted annual overall net immigration, which the Office for National Statistics estimated at about 500,000 last year, to be capped at 100,000. She said last October that her “ultimate aspiration” would be to get it down into the tens of thousands, while the Conservatives’ 2019 manifesto made a commitment that “overall numbers will come down”. Braverman insisted that Rwanda was “safe for refugees” despite being asked about an incident in which, Kuenssberg said, police shot live rounds at a group of refugees and 12 people were killed at the Kiziba refugee camp in 2018, according to the UN. She said she was “not familiar with that particular case” despite it being mentioned in the government’s own assessment of the Rwandan asylum system – and that refugees would be able to protest against their living conditions while in the country. However, she was unable to say whether she would reverse the controversial deportation policy should a similarly serious incident happen to refugees in future.