The home secretary has said anyone vandalising the Cenotaph on Armistice Day “must be put into a jail cell faster than their feet can touch the ground”.

Speaking exclusively to Sky News, Suella Braverman said she doesn’t want to “undermine” the police process by banning pro-Palestinian protests planned for Armistice Day next weekend, but that behaviour on the marches had been “utterly despicable”.

Police arrested 11 people on Saturday during a fourth week of pro-Palestinian protests in central London.

Pushed on her controversial language after using the term “hate marches”, she said “everybody is entitled to freely express their views” but said there is “no excuse… when that expression crosses the line into hate speech”.

She also confirmed she had never in her life attended a demonstration herself.

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Rishi Sunak has voiced concerns about the prospect of pro-Palestine protests on Armistice Day, with the prime minister saying such a move would be “provocative and disrespectful”.

It comes amid reports tens of thousands of demonstrators are planning to take to the streets to call for an immediate ceasefire in Gaza on 11 November. Demonstration organisers have pledged to avoid the Whitehall area where the Cenotaph war memorial is located.

The home secretary was speaking from the Greek island of Samos, where she has been learning about the government’s approach to illegal migration.

On Friday she visited a 120km long fence at the country’s land border crossing with Turkey, and on Saturday she was taken on patrol with the Hellenic Coast Guard off the coast of Samos.

Nearly a million people crossed into Greece by small boat in 2015, compared with 12,700 last year – fewer than the number of small boat crossings in the English Channel.

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The home secretary said she was “not claiming success at all by any means yet” on her pledge to stop the boats, but refused to set a target for where she would like the numbers to be by the general election.

She said it would be “pretty obvious” if the pledge had been achieved.

Ms Braverman said the UK could learn from “a policy of deterrence, tough measures, bold measures with a focus on making it clear that illegal arrivals will not be tolerated” in Greece.

However, Greece’s approach has been criticised, with EU authorities calling on an independent inquiry into so-called “pushback” tactics.

The home secretary said: “No one’s talking about doing push-backs in the English Channel”.

Commenting on the trip, shadow home secretary Yvette Cooper said Ms Braverman had “headed overseas to distract from her shameful failures back at home”.

“The Tories have created chaos in our immigration system, with a record high asylum backlog, a 70% drop in removals and thousands of people stuck in hotels, costing the taxpayer an eyewatering £8m a day,” she said.

“Instead of trying to fix the mess the Tories have created, the home secretary boasts about her failing Rwanda scheme, which has already cost over £140m, without anyone being sent.

“Once again, Suella Braverman offers no answers, but instead seeks to stoke division and blame anyone other than her own government for the failure to deliver.”