Running between buzzing Soho and grand Trafalgar Square, London's Charing Cross Road is one of the most expensive streets in the world. It is a land of hotels and high-end restaurants, where few would dream of living. Yet tucked away behind a theatre sits a row of council flats. For rent as cheap as any you are likely to find in London, a relatively poor citizen can sleep just a stone's throw from Nelson's Column.

In many other cities, this would be unthinkable. The landscapes of Paris and Washington DC, for instance, are starkly split between a wealthy centre and a ring of poor, troubled suburbs. London is different. A short stroll can take you from grimy, poverty-stricken terraces to some of Europe's most luxurious neighbourhoods.

But the city is changing. Property prices have been rocketing for years, while previously neglected areas are developed into sleek modern apartments. Some feel that life in the capital is becoming the preserve of a wealthy elite.

Now a city council in an area with a shortage of affordable housing has started efforts to relocate five hundred of its poorest residents. Some families have been asked to move to new accommodation 160 miles away, in the northern city of Stoke-on-Trent.

Some blame the government for limiting housing benefits and making the struggle to find homes even harder. Labour leader Ed Miliband controversially labelled the measures 'social cleansing.' The deputy prime minister, Nick Clegg, responded just as forcefully, saying that Miliband's comments were 'deeply offensive.' Even for a political row, the language was harsh.

The debate has surfaced with perfect timing: in ten days, Londoners will go to the polls to elect a new mayor. Affordable housing will be one of the hottest issues of the candidates' campaigns.

In the last thirty years, London has become perhaps the world's most powerful financial hub. This has brought wealth, but it has also forced up property prices. For many poorer Londoners, owning a home is now an ever more distant dream.

Londoners threatened with relocation are angry and upset. Some of these people have lived here for generations, they say - the government must ensure that they are not turned out to distant regions just because bankers or businessmen can pay more. The city is sacrificing its history, they say, on the altar of materialism and greed.

Nonsense, retort government ministers. Some of these people are unemployed; why should they be given money to help them stay in desirable areas while working families are denied the privilege? This is no crusade, they say - just fairness and common sense.