Three new admissions were already waiting when they arrived in Dover. Nine-year-old Peter Meyer (later to become famous as the film-maker Peter Morley) had arrived days ahead of the school itself with his elder brother and sister.
"We had been sent to England when our parents separated in 1933," he explains. "We were standing on the quayside waiting for them on October 5 and went off with them in green charabancs to start a whole new life."
Essinger, a Jew who developed Quaker sympathies, rented and later bought a manor house near Faversham in Kent, where she installed several of her teachers from Germany and took in English children to help make ends meet.
"She liked having kids who spoke English without an accent and whose parents could be counted on to pay the fees," explains Martin Lubowski, who like many subsequent pupils arrived during the war.
Speaking German in class was banned even before English-born pupils started joining the rolls. "I credit our nursery teacher, who taught us perfect English, for the fact I speak without any accent," says Bourne.
"I still remember a few of us youngsters huddling in a field full of excitement at having learnt what we thought was our first English swearword - 'shut up'!"
The impoverished school, where pupils had to wash pots and pans, clean the loos and help repair furniture between their studies, nevertheless produced many distingushed graduates. They include the artist Frank Auerbach, humourist Gerard Hoffnung, Helmut Sonnenfeldt, who became an adviser to Henry Kissinger, and immunologist Leslie Brent.
Professor Brent considers himself the least likely to have succeeded, given that the school eschewed science teaching because they couldn't afford laboratories. "But in spite of that, an astonishing number of us went on to become doctors and scientists, and I put that down to a really solid early education," he says.
Anyone who wonders how a woman with a troop of refugee children with limited means set up school abroad without missing a beat underestimates Essinger, he adds. "TA, as she was always known - it was short for Tante Anna - was a truly formidable woman. She was very stout, stern and not that good with children, but she had their welfare absolutely at heart."
Essinger, the eldest of nine children, studied at American universities, where she became impressed by Quaker philosophies. She opened a school in rural Herrlingen in Germany, in 1926, with two of her sisters, believing tranquil surroundings were the best setting for learning. Avoiding actual teaching in favour of organisation, she embraced a liberal educational path known as Reformpedagogic, in which pupils were considered to be equal and community spirit was fostered above all.
While exam results were always excellent, Bourne considers it a miracle he passed his School Certificate. "I had to sit it with five other pupils in 1940, six weeks after the school was evacuated to Shropshire, and we lost a fortnight's education helping with all the loading and unloading."
Brent, who arrived later on the first Kindertransport of 1938, enjoyed the benefit of some of the finest teaching. The school benefited hugely, he says, when interned Germans were released providing they agreed to work at one address for the remainder of the war. "So we got an astronomer who taught maths, a theatre director who was employed as a stoker but produced some excellent plays, and a gardener who treated us to some wonderful piano recitals."
The teachers who came from Germany with Essinger were idealists who were happy to teach "for peanuts", remembers Bourne, who went on to become an inspector for the Inner London Eduation Authority. But he laments the deterioration of the food when the cook, the single member of domestic staff employed, was interned. "Even during rationing she made us excellent meals - wonderful dishes we were familiar with, like streuselkuchen (a traditional cake)," he says.
The fact the school closed in 1948 after relocating back to Bunce Court in Faversham is believed by some alumni to be due to the fact that Tante Anna, in spite of being nearly blind, felt unable to hand the reins over completely to her successor.
But despite the fact most pupils spent less than 10 years in the classrooms, such was their affection for the place, they could not stop going back. "I returned at every opportunity," remembers Brent, who left "when money ran out for me after School Certificate - our fees were paid by the Refugee Committee."
"I feel I am walking on holy ground whenever I visit Bunce Court," adds Lubowski, who points out that reunions continued to take place for 55 years after the school closed its doors.
He does not regret missing his barmitzvah, along with his twin brother Gunther, in a school which held a political evening every week but regarded religious education as just another curriculum subject.
"Which is not to say Anna did not call us in to discuss our barmitzvahs, but we agreed to postpone it for a year, and let sleeping dogs lie when she forgot to remind us about it."
Lubowski's family perished in the camps, like so many of the parents who trusted Essinger to give their children a safe and productive start in life. Many turned their backs on religion, though not their cultural affiliations. Lubowski, a fervent Zionist, spent years on a kibbutz and in the Israeli army, while Brent later decided to make his birth surname, Baruch, his official middle name.
Morley, whose very first film was a documentary he made about the school, says it was the ethos of Bunce Court which made it a substitute home for the many children who lost their families. "Anna Essinger created a place in which teachers and pupils truly became one. We all looked after each other, and that created an enormously happy feeling of belonging."
Essinger died at Bunce Court, where she stayed on until her death in 1960, with no idea that she would be commemorated one day in Germany. Her story is told in the museum at Herrlingen, where her school was seized by the Nazis in 1934 and given to Field Marshal Rommel as a country home.
