However, though uniform for children so young is unusual, this is no pre- school "hothouse" aiming to teach young children to read and write by the time they are five.
Sarah Johnson, headteacher of the London pre-school, often feels she has to educate the parents, who, anxious to get their children into the best independent schools, want her to teach reading and writing.
But the Montessori-trained headteacher said: "I do not want parents to feel the children are under pressure to learn here. They have long enough when they are older sitting behind a desk."
However, the school does encourage three and four-year-olds to read and write if they are ready for it.
Like many independent schools, Hendon prep is under pressure from working parents to take two-year-olds, and is about to start a waiting list.
The school, which is in an affluent area, opened its doors to two-year-olds in September 1995 but stipulated that all had to be toilet-trained. This September, however, the school is expanding into new premises and will be able to accept two-year-olds in nappies.
There are 91 children in the pre-school, 27 of whom are aged two. Almost two thirds of the children come from homes where both parents are working, but only four of the 27 are at the school five full days a week from 8am to 6pm.
The 12 schedules the school offers the children range from two mornings a week to full-time. Some parents working full-time use both the pre-school and a nanny or granny.
The child-teacher ratio is 8 to 1, and staff hold National Nursery Examination Board and Business and Technology Education Council qualifications. Pre-school fees for a full-time place are Pounds 554 a month.
The pre-school lay-out is similar to that in any state nursery or day care centre - areas for sand, water and painting and areas for eating, playing and learning. Outside, an enclosed wooden adventure playground is equipped with trikes and scooters. And when the two-year-olds need a nap after lunch, one room is cleared for their mattresses and blankets.
Both Miss Johnson, and Trevor Lee, head of the prep school, believe that two- year-olds benefit from mixing with other children.
Mr Lee said: "We can understand where Paddy Holmes [the head who condemned full-time nursery care for two-year-olds] is coming from but times are changing.
"We have a new millennium and new patterns of care. As a result of that we have to make sure that in the education we provide, the children have a quality experience. It is essentially social-based but hopefully leading to academic skills and understanding."
According to Mr Lee, when a parent says good-bye to a child at the pre-school, that does not constitute a separation. The bond between the parent and child is still there.
The pre-school's motto is "Safe, loved and learning", and Miss Johnson is well aware that the difference between two and three-years-olds is great. The children are split into two classes of three and four-year-olds, a reception class for the fours and one class of two-year-olds, but they also play and learn together for part of the sessions.
"With two-year-olds, a number have never been anywhere else, so their first days at school have got to be gentle. They have got to feel comfortable. It is very much based on play, letting them choose what they want to do. Lots of cuddles. A happy, friendly, warm atmosphere," said Miss Johnson.