Mr Bancroft (48), a property manager and part-time caretaker at the school, died from an acute heart attack as a result of a pre-existing medical condition.
He had previously battled cancer and suffered a heart attack three years ago.
He died after calling out emergency services to a fire which extensively damaged a Glencoe Rd property - belonging to international yachtsman Russell Coutts - on the station where he worked.
Arrowtown School principal Robin Harris said pupils and staff were "absolutely reeling".
It was a double blow for the staff as Mr Bancroft's wife, Helen, was one of the teachers, he said.
Mr Harris said Mr Bancroft was "a tremendous guy, very generous and big hearted".
He had a very positive nature, was fun to be around and was popular with the children.
"Class teachers informed the children on [Tuesday] morning. The children were obviously affected because Phil knew many of them and particularly the older children certainly felt his loss.
"He used to do a litter patrol at the end of the day and he turned it into a treasure hunt. It was a fun thing for them to pick up litter while searching for a lucky prize card. It was his idea and it worked very well."
Mr Harris said pupils had the freedom to recognise the loss of Mr Bancroft in ways appropriate to their age and organised by teachers.
Many would be making cards, which would be passed on to the family.
"Next week we'll be having a special assembly to mark the event."
Mr Bancroft was an active member of the Wakatipu Yacht Club for several years and was keen on fostering young people's interest in sailing, commodore Mel Gazzard said.
"We'll miss Phil. He did a lot of work for the club. He was well qualified in the yachting field and had been working as officer of the day for the yacht club regatta and the annual Donald Hay race."
In a statement, Mrs Bancroft said her husband had not been feeling well on Monday and the shock of seeing the fire at the Glencoe Rd house could have exacerbated his condition.
"It was really one of those sad and unfortunate things that sometimes happen. He was not fighting the fire when he died. He simply called the services.
"Together with our children, Natasha and Mathew, I've been really humbled and heartened by the support we've received since Phil died."
Mrs Bancroft has asked for any donations to go to the National Heart Foundation of New Zealand or the Cancer Society of New Zealand.
Fire investigation officer Mike Cahill told the Otago Daily Times yesterday his inquiries into the cause of the blaze were continuing.
