“It’s quite something when you give somebody a box of tampons and they break down in tears.” Nigel Webster, the project manager of the Bestwood and Bulwell food bank in Nottingham, says he has been warning for years about “period poverty” – when women and girls struggle to pay for basic sanitary products on a monthly basis, with significant impact on their hygiene, health and wellbeing.

“I first became aware of it when a middle-aged man asked in embarrassment for his teenage daughter,” Webster recalls. “A young father came in recently asking for maternity pads for his wife who had just given birth. If you’ve got no money to feed yourself then you’ve got no money to wipe your backside either.”

This is the hidden side of poverty, says Webster: struggling to feed your kids, heat your home, but also keep yourself clean. “I remember one woman said: ‘It’s not the hunger that gets us, it’s the lack of basic hygiene.’”

While the demand for women’s sanitary products has been evident to food banks and homeless shelters for some time, the recent focus on the humiliating consequences of period poverty in the Ken Loach film I, Daniel Blake, and by politicians in the Scottish parliament and now Westminster, is bringing menstrual inequality into the open for the first time.

This week campaigners have been joined by a cross-party group of MPs – including Paula Sherriff, the shadow minister for women and equalities, – to press Procter & Gamble, one of the country’s largest manufacturers of sanitary products, to donate a small proportion of its output to homeless shelters across the UK, following anecdotal evidence of women forced to use newspapers, socks and toilet rolls instead.

Sherriff also plans to raise the issue at a meeting with Boots on Wednesday.

Led by the tampon tax champion Laura Coryton, who successfully persuaded the government to scrap VAT on sanitary products in 2015, the lobbying will highlight the Homeless Period project, which aims to increase the donation of sanitary products to homeless shelters.

Coryton is hopeful of a positive outcome, pointing out that P&G already operates a number of similar donation programmes, and has form in adopting proposals that provide poorer families with everyday essentials.

She also believes such campaigns are changing public attitudes towards menstruation. “When I started on the tampon tax campaign, people were so weird about it, and when it was first brought up in parliament no politician wanted to say ‘period’ or ‘tampon’. People are definitely becoming less squeamish,” she says.

The Scottish parliament held its first debate on period poverty in September, tabled by Monica Lennon, Scottish Labour’s inequalities spokesperson, who has championed the issue since her election last May as the MSP for Central Scotland.

“It is an uncomfortable truth that not every woman and girl in Scotland can afford to buy essential feminine hygiene products when they need them,” Lennon told the chamber, detailing evidence from Barnardo’s Scotland, Scottish Women’s Aid and the Trussell Trust, as well as from private conversations with volunteers at food banks, churches and teachers across her constituency.

“What use is a free prescription for period pain relief if low pay and insecure zero-hours contracts are forcing menstruating women to stuff their pants with toilet paper? What difference will the ‘attainment challenge’ make if you are a girl sitting in class with the embarrassment of a saturated sanitary towel between your legs?”

Since September, Lennon has continued to press the SNP government to undertake a comprehensive assessment of the accessibility and affordability of feminine hygiene products, as well as investigating the potential of free provision in the same way that free condoms are offered in a variety of public outlets but tend only to be taken by those most in need.

Lennon’s campaign has attracted the support of Paul Laverty, the screenwriter of I, Daniel Blake, who told the Guardian about the inspiration for the scene in the film in which the female protagonist is caught shoplifting tampons. “It started off with one young woman who told me that she had been sanctioned on several occasions and that she stole some stuff and the shame that she felt, but she was desperate and isolated.”

Lennon has also enjoyed cross-party support: indeed, SNP MPs and MSPs have proposed a similar scheme called the S Card, which could be handed to a local pharmacy, doctor, or nurse in exchange for a pack containing a monthly supply of sanitary products.

Ewan Gurr, the Scotland development officer for the Trussell Trust, believes the Scottish government is willing to tackle period poverty, although inevitably questions of funding – in particular in relation to newly devolved welfare powers – come into play.

Since the Holyrood debate on the subject, Gurr has met the Scottish health minister, Aileen Campbell, who stressed the need for more empirical work to be done. He now plans to work with other women’s organisations to build a research base over the coming six months.

“My sense is that there is an openness from the Scottish government, but they have to have evidence to back it up,” says Gurr. “This issue is beginning to build traction. Ken [Loach] and Paul [Laverty] captured an experience that has been going on in food banks for many years and prompted public outrage. We need to build on that now with research and action.”

While multinational donation schemes and universal government schemes require longer-term pressure, local services are piloting their own imaginative solutions.

On the Whitehawk estate in Brighton, food bank staff became aware of an urgent need for sanitary products, in particular among younger women.

“Younger women were coming in surviving on one tampon a day, with all the health implications that involves,” explains Kate Tennant, a coordinator. “It results in bullying and in not smelling so great. Young girls are living in homes where often the mother or carer is not available to offer help with periods, so youth leaders are also giving out information.”

After persuading a female trustee of the food bank to give funding for sanitary products, Tennant now runs a scheme called Monthlies. Mostly younger women are given a card that is marked off every month in exchange for a pack containing a box of tampons, day and night-time towels, deodorant, wipes and a bar of chocolate.

Tennant believes that ultimately the Department for Work and Pensions should fund GPs and health centres to distribute sanitary products to those in need, in the same manner that those on benefits are exempt from prescription charges in England and Wales. “Most people wouldn’t expect it to be an issue, but then you wouldn’t think food poverty was an issue.”

In terms of government intervention, be that Scottish or Westminster, Nigel Webster is circumspect: “We’d welcome anything that helps but we’re the sticking plaster and we need to sort out the underlying causes of low pay, zero-hours contracts and so on. Let’s not make it easy for food banks to give out free sanitary products but close them down.”