A mother told the magazine that she invested in expensive gifts to ensure her son was "always on the teacher's radar".
"I expect him to come home and say he was well looked after," she said.
One unnamed teacher at a London school, whose pupils are the offspring of Russian oligarchs or hedge fund chief executives, said the expensive personal presents are in addition to the "class gift" to which each parent is expected to contribute around £90.
Janette Wallis, of the Good Schools Guide, said the gifts were often given innocently by families from countries such as Russia, China and the Middle East, which are coming to dominate many fee-paying schools but have a different approach from traditional British families. "They want to show their appreciation," she said. "In some countries generous gifts are the norm."
Some schools have introduced a cap on presents in a bid to eliminate the appearance of favouritism. John Ing, a former housemaster at Stowe, in Buckinghamshire, said the school adopted a gift register and any item worth more than £50 was put in a cupboard to be raffled. Expensive gifts were considered "vulgar", he added.
Kate Reardon, editor of Tatler, said: "The charming tradition of giving your teacher a leaving card or gift, possibly something home made, is one we've all grown up with. But we have heard from worried parents and schools alike that in some cases the gifting culture is increasingly aggressive and manipulative."
Neil Roskilly, chief executive of the Independent Schools Association, which represents 340 such institutions, said the depiction was a "gross exaggeration".
"This might only happen occasionally and members of staff are professional enough to know they must consult with the powers that be to ensure that everything is hunky dory," he said.
"All schools, whether public sector or independent, may have a tradition of giving gifts to teachers. In some schools the gifts may be worth more than at others.
"Most schools will have a policy that covers this area."