Before a capacity crowd, Manchester City hosted Arsenal yesterday afternoon in a match that showcased two of the Premier League's most exciting players, the Gunners' Mesut Özil and the Sky Blues' Yaya Touré.

The mercurial midfielders' prodigious talents earn them £180,000 a week each, wages some people may find obscene but which their clubs insist are determined solely by the invisible hand of market forces. Now those same market forces are being forensically analysed as Premier League clubs stand accused of paying "poverty wages" to their contract staff, raising questions about whether they are squeezing the incomes of cleaners and stewards so that they can afford the lavish salaries demanded by their leading players.

In a stark illustration of the fundamental inequalities at the heart of the Premier League's economy, Citizens UK, a civic alliance of more than 350 community organisations, calculates that it would take a full-time cleaner at either club 13 years to earn what Ozil or Touré earns in a week.

In a hard-hitting report published today, the alliance calls for clubs to sign up to its Living Wage campaign, under which employers promise to pay workers outside London an hourly rate of £7.65 and those inside the capital £8.80. Backed by high-profile supporters including Labour leader Ed Miliband, KPMG, and Financial Times owner Pearson, the campaign was started more than a decade ago by workers in London's East End who found that, despite holding down two or more minimum wage jobs, they were struggling to make ends meet and had no time left for family or community life. Many found they were having to commute long distances to work, journeys that ate into their wages and leisure time. This, says Citizens UK, is a familiar concern for the 300 or so contract staff estimated to work at each of the country's Premier League clubs.

Richard Poku, 19, a member of North London Citizens, was paid below the living wage when he worked as catering staff for a subcontractor serving several football stadiums, including those belonging to Tottenham Hotspur, Arsenal and Wembley. Most shifts were four hours long, paid at £6.19 an hour.

"It's ridiculous that people with kids have to come from so far away to earn basically nothing," said Poku, who accuses footballers of failing to understand that their success is built on the backs of low-paid workers. "Footballers are earning that much because people are paying to watch the matches, and we are the ones catering for them."

But, despite years of pressure stretching back to 2008, when Boris Johnson called on clubs to back the campaign, none has signed up to become an accredited Living Wage employer. Almost all have refused to meet the campaigners. Many insist it is not an issue because they use outside contractors. As a spokesman for Queens Park Rangers said: "We don't employ our cleaners directly and have no comment on the matter." Others, such as Chelsea, refuse to comment point blank.

Some executives have been more willing to outline their reasons for not signing up. Arsenal chief executive Ivan Gazidis (salary £2m) said he believed the Citizens UK campaign was "well-intentioned" but the issue was "complex and political, and in any case Arsenal benefits packages are generous in market terms".

This got short shrift from Chris Harrington, a member of Islington Citizens and an Arsenal supporter for more than 60 years: "What Arsenal must be made to realise is that the London Living Wage is right, just and economically sound and is a public policy here to stay. And that we in Citizens UK will not give up and go away."

Some will question why football clubs, many of which fail to make a profit, are being singled out by the campaign. But Citizens UK can point out that many other organisations have also been targeted. This week, for example, it is expected to take aim at John Lewis, which has faced criticism for paying its 3,000 cleaners, who are outsourced, a fraction above the minimum wage.

But many people believe that the imbalance between what the clubs pay their highest and lowest earners is so egregious that they have become legitimate targets for a sustained campaign.

"In 2008 we reported on the ethical policies and practices of the UK's major clubs and highlighted the poor pay of their less high-profile employees – catering workers, cleaners and stewards," said Katy Brown, consultancy manager at the Ethical Consumer Research Association. "Sadly, not much has changed. Not a single club is listed as a living wage employer on the Living Wage Foundation's website. Low pay is endemic in many of the UK's industry sectors, but nowhere is wage inequality more apparent than in the Premier League, where top teams still score poorly on fair pay."

The Premier League itself is reluctant to become involved in the issue. "Statutory pay levels are determined by government and all Premier League clubs adhere to them, and other relevant employment laws," a spokesman said.

But there are faint signs that some clubs are sensing how the wind is blowing and know that the scheme may become difficult to resist as more employers join up. Manchester City recently became the first club to pledge it would pay a living wage to all apprentices and interns. Nixon Tod, a City fan who has led the campaign for his club to introduce the living wage, welcomed the move: "The next step would be for City to extend that commitment to all the subcontracted staff. This would affect hundreds of people and make Manchester City the leading living wage football club in the Premier League."

A spokesman for Spurs also hinted the club was warming to the scheme: "The club have held positive discussions with organisations on progressing the living wage, including London Citizens, and are committed to reviewing our third-party suppliers, including cleaning and catering contractors, when their contracts are in a position to be renegotiated and we can ensure continued levels of employment," the spokesman said.

But little is likely to change unless the crazyeconomic tensions at the heart of the game are resolved. Ellis Cashmore, professor of culture, media and sport at Staffordshire University, points out that many Premier League clubs are "spectacularly inept" as businesses: "In many cases, wage bills are 110% of turnover. You don't need Micawber logic to realise the result is misery. But banks seem prepared to prop them up on condition that they prune costs."

Cashmore imagines a bank manager and a club owner in conversation. The manager tells the owner the club is £10m in debt and must minimise its outgoings.

"We're opting for a cheaper supplier of food for the executive boxes and giving them supermarket wine," the owner says. "We're outsourcing the programme publisher, using poor quality paper and adding 20p to the price … and we're paying our cleaners rock-bottom wages."

The manager points out that the footballers' wage bill is more than £100m. "Yes, but they're different," the owner says. "If we don't pay them, their agents will just take them to a rival club."

"Fair enough," says the manager. "Pay your players as much as it takes. But screw the cleaners."