The cleaners sweeping the floors of the central London headquarters of the Department for Work and Pensions have asked Iain Duncan Smith for a pay rise.

They say the minimum wage isn’t enough to live on unless you do two jobs, and they’re asking for the department to pay them a “Living Wage” instead.

What’s the difference? FactCheck investigates.

How much is the national minimum wage and who decides?

It depends on how old you are.

Workers aged 21 and over get at least £6.08. The minimum hourly wage is just £4.98 for workers aged 18-20, £3.68 for 16-17-year-olds, and £2.60 for apprentices under 19 or in the first year of an apprenticeship.

The sums are the same across the UK and are a legal requirement set by ministers based on recommendations by the Low Pay Commission, though some workers are exempt, for example prisoners, or volunteers.

The government body is made up of nine commissioners – three representing employers, three representing employees, two academics and a chairperson.

They consider economic factors in deciding the wage level: GDP levels, the labour market, economic forecasts, forecasts for earnings, and so on. They take inflation into account but regular rises are always up for discussion and the question of whether a rise in the minimum wage will harm Britain’s competitiveness or economic growth features heavily in deliberations.

What’s this “living wage” then?

Launched in 2001 by community activists in East London, the Living Wage Campaign says the cost of living should be taken into account when wages levels are being set.

It thinks everyone in London should get paid at least £8.30 an hour, based on various household costs including transport, housing, council tax, and the proverbial “shopping basket”.

Outside London, it’s £7.20 an hour, reflecting lower costs of living, for the most part.

Businesses who sign up do so on an entirely voluntary basis.

A new living wage will be set this year to reflect rising costs.

How do they work it out?

For London, econmists at the Greater London Authority (GLA) take an average of two different ways to calculate a basic wage – the first assumes a ‘low cost but acceptable’ household budget and calculates the wage needed for that.

Then they take 60 per cent of the median (or middle ranking) income for London. They calculate the average between the two before adding 15 per cent.

What is a ‘low cost but acceptable’ household budget?

It depends on how big your family is, whether you work full time or part time, and things like how far you live from your work, or how much your weekly shop comes to.

The GLA use four family models:

– two adults, a 4-year-old and a 10-year-old

– one adult, a 4-year-old and a 10-year-old

– a couple

– a single person.

Last year, they based living costs on how much you might have paid for housing, council tax, transport, childcare, and a ‘shopping basket’ – food; clothing; personal care; household goods and services; leisure; energy; NHS charges; insurance/pension contributions; debts and fines; costs of seeking work; pets; smoking and charitable donations.

If both members of a couple with children were in full time work, they calculate that they would pay £634.28 a week on all of the above. The lion’s share was for childcare, which came to £240.69 a week, followed by the shopping basket – £209.80 a week. Housing was £101.54, then transport, at £57.09, and council tax, at £25.16 a week.

That family, the GLA said, on a joint income of last year’s national minimum wage of £5.93 an hour, would have earned £428.10 a week with just child benefit, or £648.50 with all benefits.

Leaving a surplus of £14.30 a week if all tax credits and so on are included, but a shortfall of £206.20 a week if child benefit was the only help the family got.

How will a Living Wage affect the economy?

Those at the centre of the Living Wage campaign say because it’s voluntary, it’s not going to suddenly radicalise the British wage structure. Donald Hirsch, of the Centre for Social Policy Research, which has been working on the minimum income standard underpinning the national living wage structure, said: “We accept it can’t be done by everyone, and we don’t want to force it on everyone. Whether you can do it or not will depend on how big the company is, and how many people are on low incomes, but you can’t beat everyone with the same stick.”

Also, it’s going to change from this year, because the benefits and tax credits system will be so drastically reduced. At the moment, the living wage is offset by benefits and tax credits, and so on, which go some way towards covering living costs. When these are whittled away, Mr Hirsch accepts the jump may be too high for employers.

“Although we’re saying a living wage is needed for people to live on, we also have to be realistic. Employers are signing up to it, and we want to encourage that. We can’t just say if something changes in the benefits system, then tough, deal with it. If we can’t apply it in full, we will continue to keep track of where it should be,” he said.

The Living Wage campaign also say that workers on a living wage are more likely, on the whole, to turn up for work, give better customer service and greater productivity, and living wage employers have a lower turnover of staff.

It’s certainly gaining in popularity. Boris Johnson, Ken Livingstone, Brian Paddick and Jenny Jones all endorsed it in their London mayoral election manifestos.

What about the cleaners?

DWP says that because its cleaners are contracted by an outside agency, Mitie, they cannot set their wages. A spokesperson said: “The DWP’s cleaning service is provided by an external contractor, and they are obliged by law to pay at least the legal minimum of the national minimum wage.”

The DWP adds: “We expressly require our suppliers to pay at least the legal minimum of the national minimum wage.”

But the department is obviously familiar with the concept of the living wage, saying: “All DWP staff are paid at a rate above the living wage.”

Mitie declined to comment.

So where next?

Well, that’s up to employers. Some like it, some don’t. As for the DWP, they say they will respond to the letter from the cleaners, but we don’t yet know what they intend to say.