The daughter of the British humanitarian who organised the Czech Kindertransport operation that saved 669 children on the eve of the second world war has written to the home secretary to urge that Britain extend the same “compassion and warmth” to the child refugees of Calais.

In an open letter to Amber Rudd, Barbara Winton, whose father became known as “the British Oskar Schindler”, writes: “My father, Nicholas Winton, witnessed the appalling conditions children were enduring in the refugee camps in Czechoslovakia in 1939 and was determined to give them the chance of a better, safer life by bringing them to Britain.”

While many children returned to Czechoslovakia after the war, others, whose families had been murdered by the Nazis, remained in Britain and “became valuable, integrated citizens”, she says.

Nicholas Winton, who organised the rescue of Jewish children on what became known as the Czech Kindertransport. He died in 2015. Photograph: David Levene/The Guardian

It is estimated there are 6,000 people across the world alive today thanks to the rescue.

She wrote: “Despite some disgruntled voices, much like today, protesting the dangers of allowing into our country those from such foreign cultures, the overwhelming response was one of compassion and warmth … Even at a time when city evacuations were being planned for British children, homes were found for these vulnerable young refugees.”

Now Winton is calling on the government to do the same for hundreds of unaccompanied child refugees stranded in Calais after the demolition of the makeshift camp.

In a letter published on the charity Help Refugees website, she said: “Those who have travelled across Europe to Calais, to escape the life-threatening dangers of their home country, are hoping desperately to find the sanctuary their parents dared to believe Britain would once again offer.”

The story of what Nicholas Winton achieved did not become public until 40 years after the event, and in 2003 he was knighted for “services to humanity in saving Jewish children from Nazi occupied Czechoslovakia”.

Two women, now in their 80s, who were among those rescued from the Nazis by Winton’s initiative, have also written to the government urging that the children stranded in Calais be brought to the UK.

Eve Leadbeater, 85, was brought to Britain in July 1939 as an unaccompanied minor and taken in by a primary schoolteacher who had responded to an appeal put out by Winton.

She wrote: “In the last few months I have been putting myself in the place of those unaccompanied children in Calais fleeing their own horrors; the contrast with my own experience has left me distressed and in tears.”

She said the increased animosity toward immigrants since the referendum has left her in shock: “In 2016 do we live in the same country that welcomed me in 1939?

“I keep thinking what those children could contribute to the UK. As an honest, hard-working British citizen since 1945, I hope I have repaid some of my debt to this country by teaching children in secondary schools and working as a charity volunteer in my retirement.”

Another Kindertransport child, Dr Lisa Midwinter, said she would have perished in the Auschwitz concentration camp with the rest of her family had it not been for the “generosity of the British government”.

In a separate letter she wrote that “we must now urgently help the Calais refugee children”.

Between 1938 and 1939, a large-scale British humanitarian operation brought 10,000 mostly Jewish children fleeing Hitler’s growing threat from Germany, Austria and Czechoslovakia to safe homes in the UK.