Protesters have marched against the government’s illegal migration bill in cities across the UK on Saturday, with organisers claiming thousands had attended. Demonstrators carried signs and banners, some reading “no human is illegal”, as they matched towards Downing Street in central London. Organisers Stand Up To Racism and the Scottish Trades Union Congress (STUC) also held protests in Glasgow and Cardiff against racism, Islamophobia, antisemitism, fascism and the far right. The legislation introduced by the home secretary, Suella Braverman, means that refugees who arrive in the UK through unauthorised means, such as crossing the Channel in a boat, will have their asylum claims deemed inadmissible. Braverman is on a trip to Rwanda this weekend, for which the Guardian did not receive an invitation, to reaffirm her commitment to the government’s policy to deport migrants to the African state. Maria Frazier, 75, said she was protesting against the government because she agreed with Gary Lineker’s comment comparing the language used to promote its immigration policies to that used in 1930s Germany. The retired speech and language therapist from south London told PA Media: “We think there should be an all-out indefinite general strike and the Tories should be removed by class action. They’ve got some quite violent programmes that they’re trying to bring in – they’re trying to ban strikes, they’re deporting immigrants – it’s not British. “Lineker was right when he said there are shades of the German [Third] Reich in the methods that they’re using. “People are turning out because they’re extremely angry at the way the economy is being run and the deprivation that’s going on while the rich people in power make themselves richer.” Coachloads of protesters were pictured on social media wearing masks depicting the face of Lineker, who was due to return to TV screens to present coverage of the FA Cup quarter-final between Manchester City and Burnley. The broadcaster was taken off air last weekend for a tweet criticising the language used by ministers when discussing the government’s asylum policy. Planning officer Mark Daly, 65, who travelled from Horsham, West Sussex, said he wanted to stand against the government’s “racist” bill. “The government is trying to make these people not only unwelcome but illegal. We cannot classify people as illegal, it’s a racist policy from a racist government,” he said. Lizi Cushen, 39, said she joined the anti-racism protest London with her husband and sons, four and six, because she had been “shocked” by the scandal of missing refugee children from Home Office hotels. The architect from Leyton, east London said: “The illegal migration bill is dehumanising everyone who’s seeking asylum. It’s important to protest because it’s the only way to be visible and heard at the moment.” Her sons held signs calling for “safe passage for all kids like me”. Cushen’s friend Cassi Harrison, a 42-year-old charity worker, added: “It’s just outrageous. “We see quite a lot of the government ministers saying they speak for the great British public, and we want to be here to say that they don’t speak for us.”