Michael Gove, the Westminster Education Minister, said last week that state schools should be more like private schools, but I wonder if he has ever seen the Australian comedian Chris Lilley playing his most monstrous character, Ja'mie King?

Ja'mie, star of Ja'mie: Private School Girl (BBC Three, Thursday, 10pm), is in her final year at an exclusive girls' school in Sydney and she is funny and awkward and cringy, but she is also a reminder of what the privilege and thoughtless elitism of private education can do to a human being.

Ja'mie (she used to be Jamie but added the apostrophe in year eight) first appeared nearly 10 years ago in Lilley's mockumentary series We Can Be Heroes before reappearing two years later on Summer Heights High, and she was instantly Lilley's best creation because she felt real.

Almost everyone who has ever been to school or university will have encountered a Ja'mie: self-centred, narcissistic, privileged, insincere, hateful, ungrateful and rich.

In the new series, after many years of success at school (hockey captain, swimming captain, prefect, etc) Ja'mie is preparing to go to university to study PR and has her eyes on some of the boys in the nearby Kelton Boys Grammar.

"It's good for me to associate with the other elite private schools," she says.

"They're the future leaders of the country so it's important for me to get in with them now so I'll have connections later in life."

Of course, this is exactly what parents expect from private schools in real life, but Ja'mie has the gall to come right out and say it, and that's uncomfortable for those who support private education - which is the point.

What Lilley also does is expose the idea that doing charity work somehow makes the inequality all okay.

"I'm going to take my gap year and do work in Africa," says Ja'mie. "It's really bad over there, and stuff." She also tells us she likes doing charity work in some of the poorer areas of Sydney, where there are lots of immigrants. "They look fit because they're not eating," she says.

All of this horror comes pouring out of Ja'mie's mouth disguised as niceness and what's remarkable is how real it feels.

The fact that Lilley, 39, gets it so right playing Ja'mie, 17, and produces an impersonation rather than a drag act is partly because he saw lots of private school girls in the part of Sydney where he grew up; he also did some Facebook stalking to observe how teenage girls behave.

If there is a problem with the character having a series of her own it's that all her hatred has become exaggerated and unsoftened.

Lilley always wanted to make the point that privilege can damage teenagers - and quite right too - but in doing so he has ramped Ja'mie up a little too much.

He also appears to have forgotten one of the important themes of Summer Heights High, which is that however hateful, ludicrous, aggressive and alien the behaviour of teenagers may seem, underneath it there's usually one emotion to explain it all: fear.