As a proud lesbian feminist I have campaigned for years against the beauty industry and cosmetic surgery. I have never worn makeup, except once, as an experiment for these pages, and for years I even refused to wear a bra – until I had to dress up in vaguely smart clothing occasionally for work.

But we all have an achilles heel, and mine is facial hair. I hate it, both on myself and other women. I have a particular terror of fuzz appearing on my face, and always carry one lone item of beauty equipment: tweezers. Luckily, I am not particularly afflicted, although in recent years I have noticed one long black hair that sprouts from my left cheek, another under my chin, and a few barely noticeable ones above my lip. The second they appear they are instantly torn asunder.

My fear of the fuzz is hardly unusual. Even in the thick of the late 1970s women's movement, I remember a close friend – a fellow lesbian and hard-line feminist – confessing, "I'm so glad I discovered electrolysis before feminism!"

Not everyone shares our prejudices. A whiskers-pride movement has been growing in recent years. Across the web, there are women writing about their heartfelt acceptance of their moustaches and beards, including Debra Ann Beechy, who has written a doctoral thesis on the topic. "My mornings used to involve at least an hour of plucking in front of a lighted, magnified mirror," she writes, "Now I do not have to get up early to pluck. Elation!"

Over the past two months, a feminist activist in Bristol called Jessica Burton has been running a campaign called Hairy Awarey, asking women all over the land to go natural. "I've been hairy for so long that it just seems normal to me," says Burton, "but I do feel that at the moment women do not have a choice about hair . . . I suppose the excitement about Hairy Awarey was that the simplest of actions (leaving the razor on the side of the bath tub) can have life-changing effects for the women brave enough to try it."

The logic of Hairy Awarey is that if enough of us give up the tweezers, the sight of body and facial hair on women will be normalised and any stigma will eventually disappear. But is it really that easy? If a hardline anti-grooming feminist such as me has an aversion to excess hair, how many women are really going to embrace it?

Some already do. Shazia Mirza, the comedian and columnist, grew her body hair over a period of seven months for a BBC3 documentary called Fuck Off, I'm a Hairy Woman. "At first I thought I wouldn't be able to do it," she says, "as I was obsessed with hair removal, having had a Hitler moustache since I was seven. But actually it was very easy. Having body hair is the most natural thing. We are all hairy, and it is a myth that men like hair-free women. After the programme I had thousands of emails from men who said they much prefer hairy women – but they can't say that in public because lads' mags tell them they have to like a hair-free Abi Titmuss."

Lisa Spirulina, a lesbian of Indian heritage, tells me she is proud of her moustache. Spirulina's dark skin obscured her facial hair until it became more abundant in her late teens, so "I got away without being bullied at school about it," she says. "Now I am proud of my hairy lip. I sit playing with it when I am thinking, or watching TV."

Del La Grace Volcano, formerly known as the lesbian photographer Della Grace, grew her goatee beard in the late 1990s to much media consternation. "I lived for a year with a beard before I decided to take testosterone, not to be seen as a man but to make my intersex-ness visible," she says. "It was rough always getting negative vibes from people, knowing they were judging you and/or uncomfortable. I know quite a few women who have facial hair and are happy about it. I know more women who are ashamed and bothered by it." She says that all the women she knows who feel empowered by their facial hair identify as lesbians.

An estimated 40% of all women naturally grow facial hair, and the campaign We Can Face It was launched in June, backed by Dr Dawn Harper from the Channel 4 series, Embarrassing Bodies. It aims to create a supportive community for women with unwanted hair.

According to a survey of 1,000 women carried out as part of the campaign, 30% of women with unwanted facial hair suffer clinical depression, a quarter believe facial hair has held them back from promotion, and more than 40% say it has affected their ability to form relationships.

Most women self-treat the problem by tweezing or shaving, and the only body hair most women like is their eyelashes and eyebrows. The We Can Face It survey found almost all the respondents felt negative about their facial hair, with more than half feeling anxious to very anxious if it was visible and couldn't be removed immediately. Two thirds said it made them feel "unfeminine".

Female facial hair has a number of causes. Aside from hereditary factors, it can also be caused by an excess of certain testosterone-related hormones or polycystic ovary syndrome (POS). Jessica Karjala discovered she had POS after being alerted to the fact that a sudden facial sprouting can be a symptom of the disease. "When I experienced an increase in facial hair it was coarser and thicker than usual," she says, "and I removed it out of vanity. I chalked it up to middle age or perimenopause. I wish I had known that my increase in facial hair was an early symptom of a harmful hormone imbalance. Regardless of your comfort level in regards to your appearance, [that knowledge] could prevent serious future health problems."

Philippa Willetts also has excess facial hair as a result of POS and says she "wants to be less horrified by it. I've known some women with more facial hair than most who looked fantastic, and I envy them their confidence. Years ago when I started gaining weight (also as a result of POS), and was unhappy about it, a friend said I was also judging other fat women. I agree, and think it is the same with facial hair. If I hate it on me I must hate it on other women. We have no idea how many women grow hair on their face, because the vast majority will pluck it out. I talk to all my friends about other beauty issues, but this is a big secret between us."

Women can grow more accepting of their facial hair with time. Julia Long, a feminist academic in her 40s, says she "started to grow a bit of a 'tache when I was 12, when I hit puberty. At school I would be bullied by the boys who made me feel horrible about myself." She decided to undergo electrolysis after reading a magazine article about it, but her GP told her she would have to wait until two years after puberty if she wanted it to be effective. "Two years to the day I started the treatment," she says. "It was agony, and left me with a Ribena-coloured rash on my face that was more noticeable than the hair."

So is it possible to free ourselves from this prejudice? In Italy there is a famous saying, Donna barbuta, sempre piaciuta – everyone loves a woman with a beard. Could that be the case in Britain? Burton hopes so. She plans to make Hairy Awarey an annual campaign. And after spending "hundreds of pounds" on bleach, wax and creams over the years, Long has now decided to let her hair grow. "Maybe it's because I am 40, and men look at me less, but I feel so much better now I am letting it all grow out."