Home secretary Suella Braverman has been accused of “whipping-up hate” by characterising small boats crossing the English Channel as an “invasion” – but her rhetoric has won applause from Nigel Farage.

The under-fire minister used a Commons statement on the chaos surrounding the Manston migrant holding centre in Kent to deliver inflammatory comments that were widely condemned. They came a day after another holding centre in Dover was petrol bombed.

She told MPs: “Let’s be clear about what is really going on here: the British people deserve to know which party is serious about stopping the invasion on our southern coast and which party is not.

“Some 40,000 people have arrived on the south coast this year alone. Many of them facilitated by criminal gangs, some of them actual members of criminal gangs.

“So let’s stop pretending that they are all refugees in distress. The whole country knows that is not true. It’s only the honourable members opposite who pretend otherwise.

“We need to be straight with the public. The system is broken. Illegal migration is out of control and too many people are interested in playing political parlour games, covering up the truth than solving the problem.”

Braverman later agreed with suggestions from Tory MP Lee Anderson that some migrants can “get on a dinghy and go straight back to France” if they believe the accommodation in the UK is not good enough.

The Refugee Council described the home secretary’s comments as “appalling, wrong and dangerous”, and Labour MP Zarah Sultana hit out at language that “whips-up hate and spreads division”. “She’s totally unfit to be home secretary,” she added.

But she won the support of former Ukip and Brexit Party leader Farage, who said on Twitter: “Suella Braverman, who is under attack from Remainers and the globalists, has said what is happening in the Channel is an invasion. It’s a word I’ve been using for two years and been condemned for.”

He added: “Believe me, the Establishment are out to get her because she’s got the guts to say many of these people are just not refugees. Well done her.”

The Channel crossing crisis has deepened amid growing concern over the conditions in which migrants are being held while waiting to be processed once they arrive in the UK.

Conditions at the site at Manston were last week described by independent chief inspector of borders and immigration, David Neal, as “pretty wretched”.

The home secretary said around 40,000 people have arrived on the south coast of England in 2022, more than double the number of arrivals via the English Channel in 2021.

Braverman also defended her decision to keep thousands of people at the migrant centre after some of her colleagues accused her of deliberately ignoring legal advice to transfer people from the site to hotels.

Intended to house around 1,500 migrants for less than 24 hours at a time, numbers have swelled to more than double that, with one Afghan family saying they had been there for 32 days.

Braverman was reappointed by prime minister Rishi Sunak last week, six days after she resigned from the same role for sending a government document from her personal email to an employee of a member of parliament in breach of the rules.

Opposition parties and even some members of parliament in the governing Conservative Party have questioned her suitability for the role.

On Monday, Braverman acknowleged she had sent official government documents to her personal email address six times, raising fresh concerns about breaches of ministerial rules while in charge of the nation’s security.