Welcome back Carrie, welcome back Sarah, hope you haven't started getting your hair done since we last saw you.

Carrie Mathison, the CIA agent with bipolar disorder played by Claire Danes in Homeland, and Sarah Lund, the glum, emotionally constipated Danish cop portrayed by Sophie Grabol in The Killing, return to British screens this Sunday and next month respectively, and we'll be delighted to have them back.

If you're not familiar with their characters, Carrie is fanatically committed to her job, lacks self-awareness, veers between overbearing pushiness and intense vulnerability, and spent series one trying (and ultimately failing) to hide her mental health problems from her bosses. Sarah, meanwhile, is awkward, gruff and tight-lipped, short on people skills and completely hopeless at managing the work-life balance; you suspect she might have undiagnosed depression. Both are courageous, but make spectacularly bad decisions at times. Neither actress is Botoxed, pumped or preened and they don't change their outfits every two minutes (Lund famously alternates two jumpers and never changes her jeans).

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In other words, they are women with baggage, women with frailties as well as formidable strengths, women who give their clothes the sniff test in the morning rather than worry whether their shoes match their bag. Above all, they are extraordinary, loveable, desperately needed antidotes to the hopelessly hackneyed two-dimensional female characters that we see far too often on TV drama, characters that are supposed to portray a strong, liberated version of post-feminist womankind, but too often end up as cardboard pastiches that patronise women.

You know the sort I mean: sassy, sardonic, tough, beautiful, stylish, resourceful; think Lara Croft transposed into lawyers' offices, police headquarters and suburban homes. Think Amy Pond in Doctor Who, Emily Thorne in Revenge, any of the female leads in Silent Witness or Waking the Dead, Kate from Lost, Kalinda in The Good Wife; I could go on. It's not that there is no room for the kick-ass, glamorous woman (the male action hero with breasts); in fact, if she didn't exist, people like me would be complaining we needed to invent her. It's just that it's boring and irritating to encounter her in nearly every drama. Even characters who are ostensibly less cartoonish, such as the Desperate Housewives or Alicia in The Good Wife, women who have supposedly experienced difficult divorces or drink problems or childhood abuse, are still unrealistic. Their past traumas bounce off them and their glib, unflappable exteriors rarely waver.

Those shoehorned into other flimsy stereotypes – the stay-at-home mum for instance – must also go through a goddessing process. In Desperate Housewives and Mistresses, both now over, Bree and Trudi couldn't just be mums with mums' concerns, they had to be Jane Asher. When the scriptwriters wanted to develop their characters, their muffin-making could be neatly turned into a blockbuster business in the space of a few episodes. What came out at the end was something depressingly familiar – the perfect, immaculately dressed uber-babe who is lusted after by younger men, makes loads of wonga and always has time for cards or cocktails with the girls.

Of course, the role of TV, partly, is to provide us with untaxing entertainment and these shows provide that. Fine. It's just that audiences don't want to be fed that nonsense all the time. Sometimes we want characters to connect with. Soap operas have always been pretty good at this, but prime-time drama is hooked on vapid caricatures of women. It's as if screenwriters – often men – are afraid to portray a woman's flaws and weaknesses, in case they're accused of being regressive and sexist.

Having a version of Wonder Woman in every show has another annoying consequence: it leads to the portrayal of male characters as weak or inadequate by comparison, like Rory from Doctor Who or the awful Richard in Mistresses. Pity the actors who play the dithering, drippy sidekicks.

So here's to Carrie Mathison, Sarah Lund, the wonderful Lol from This Is England and Sue Brockman from Outnumbered, versions of whom we could actually imagine meeting in real life. People are complex and flawed, they have strengths and weaknesses, and we audiences seem to like them that way.