Margaret Thatcher loved the maquette of Canary Wharf. She listened enthralled as the architects explained how a light railway would extend through the razed old docks.

There was a toy train running round the mock-up. The whole thing was over 10,000sq ft. The little railway ended in acres of suburban housing. Little red-brick cottages arranged in geometrical closes and perpendiculars. The developers explained to the Prime Minister that this was where commuters to the financial towers would live. Just 20 minutes away from work and on the water's edge. All of them property owners. She adored the architects' model dream.

The Docklands Light Railway still has the feel of a scale model. The stations sound as if they were named after pubs: Royal Albert, Royal Victoria, Galleon's Reach. But the high-rise housing over the easternmost spur of the DLR has seen happier days. Dirty England flags hang from balconies. Panoramic vistas over gargantuan retail parks. The Millennium Dome (now the O2) is filthy, begging to be torn down.

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Beckton is the end of the line, rebuilt for a middle class that never arrived. Now superimpose a poverty map of London over a Tube map. Dark red runs along the line to Beckton. More than 60 per cent of the children here grow up in poverty. But there is worse data. London is statistically parcelled up into 4,772 micro-areas. Beckton is the tenth most deprived. Twenty minutes from the headquarters of HSBC.

Beckton doesn't look foreign at first. The unkempt trees leering over cracked pavements. The locals-only pubs. Dreary parking lots. It looks like the abandoned set of Brookside. But it sounds like a foreign country. Everyone exiting the station ticket barriers is talking Polish or Bengali, Lithuanian or Romanian.

Immigrant London used to be found within Tube zone two. It used to be about Bangladeshi Spitalfields and Jamaican Brixton. Right through the 20th century, one trend held steady: immigrants began in the decaying inner city, while the white working class moved out to Kent and Essex. This is not how immigration works any more.

There is a whole Eastern European city in London. This city is bigger than Sheffield, with more than 500,000 people. More than half are from Poland. More than 80 per cent have arrived since 2004. These are people from Lithuania, Romania, Bulgaria and the other poor countries that joined the EU then or later. This is a city working in basic jobs. But it also has its Russian aristocrats and tens of thousands of professionals, not to mention refugees from Bosnia and Kosovo.

Most live in zone three. Places such as Beckton. Here, old whites sip Carling lager resentfully in the afternoon pubs. Escapees from the inner-city degeneration of the 1980s, they have been dealt a cruel turn of fate by the metropolis. The DLR dream brochure they bought into has turned into a place less than 50 per cent white British. Unable to afford a reverse white flight, grittier types take to wearing England football shirts at every occasion. Eastern Europeans make up about 20 per cent of the Beckton population, Bangladeshis a further 25 per cent.

I entered a hangar-sized Lithuanian supermarket. Lithuanian mothers pushed trolleys down aisles of pickles of mindboggling size. There were tables of activists getting out the vote for a Lithuanian fracking referendum. Blue tracksuits lounged in the Lithuanian café-grill. There was everything a Lithuanian might need. Grotesque Russian paintings were being exhibited on the second level where there was a small bookshop stocked with Lithuanian tomes and anti-Putin pamphlets.

Three women were sitting at a kiddies' table in the middle, having tea. Chopin tinkled in the background. "I don't live in Britain," the owner said. "I live in Lithuania. I watch Lithuanian TV. I use the internet in Lithuanian. My friends are all Lithuanians. This shop is Lithuanian. I only meet Lithuanians. The only thing I do in Britain is pay taxes to the British."

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Beckton empties between 6 and 7.30am. The first trains belong to Africans and Eastern Europeans. Africans have sewn up industrial office cleaning. Poles, Romanians and Lithuanians have tied up building. Because they are reliable and recommend their friends, these jobs are rarely advertised in English. Their girlfriends dominate house cleaning and waitressing.

In the morning darkness past illuminated Canary Wharf ride the bleary-eyed renovators of a city they barely understand. Men such as Jurek, a phlegmatic Polish labourer from Gdansk. He commutes in every morning to Kensington. London construction is a game for the rich. There are no jobs building office blocks and data centres in the suburbs but they are three a penny digging basement ballrooms in the Royal Borough.

Back home, Jurek used to work at a sewage treatment plant. He would daydream about EuroMillions. They sacked him. He had always loved gambling. So after three days drinking he got on a night bus, without any real plan. He woke up at Victoria Coach Station – our miserable Ellis Island. Poles he met there told him that their foreman needed extra labourers. The pay was only £5 an hour but it was in a good area.

Jurek was gobsmacked by the white wedding-cake mansions this Perivale Polish company was renovating. They had columns like ancient temples over the doors. Floral stucco mouldings rounded the ceilings. He was also surprised that everyone who lived in Arcadia appeared to be Filipino. Every morning, a busy little woman would unbolt the lower ground door and dash out to stock up on brass polish. Jurek would make a point of greeting her: "Good day, Madam." He imagined her to be an oligarch's wife. But she would giggle and rush inside. "Thank you, Mister." He did this for about a month until one of the bricklayers took him aside. "The owners are in Russia, dipshit. The gooks are the maids."

I worked on a site in Pimlico. My job consisted exclusively of loading rubbish. There is more of this on a building site than you can possibly imagine: wood shavings and plaster drippings, untold chunks of MDF, boundless rubble, foam wrapping and glass shards. Renovating a £2.5m flat for £7 an hour was a bunch of dreamers. There was Stas, who in his 10 years working in London had learnt only 12 words of English, most of them swear words.

For 10 years, he had sworn at co-worker Jacek, a spindly painter from Krakow who knew maybe 20 words of English, all of them paint-related. They were both like sailors, renovating London for nine months and then back to Poland.

Jacek was here because his daughter had Down's syndrome. Every pound he could spare was sent back to pay for her care home in Germany. He welled up explaining that there are no such institutions in Poland. Jacek's sacrifice meant that at the age of 50 he had shared damp rooms his entire adult life.

Lunch brought Stas and Jacek out of their squabbling and into conflict with the youngest labourer in the team, a grumpy, heavyset joiner whom both inexplicably called Miner. He was a newcomer, in England only since 2009. Miner knew some English. Just about enough to read.

He was, like almost all builders, an obsessive saver. But unlike the rest, he was neurotic about it. He was always on his mobile phone calculating the precise value of his savings. This was because like many of the young ones he thought he was only here temporarily. He was saving to build a house, a dream mansion.

Miner needed £30,000 but the exchange rate and the influx of Romanian workers were working against him. He rolled a cigarette. "Those Romanians are a bunch of uninsured cowboy builders! They are driving down our wages. They're working for £4 an hour. Britain is mad to let them in."

If Conservative MPs ever deigned to talk to Polish builders they might discover people near-identical to the Norman Tebbit fantasy of the working class. Industrious savers. Family people. Willing to work for nothing. Fans of Thatcher, the Soviet-fighter. Disgusted by trade unionists and completely depoliticised.

Polish churches are full every Sunday. London was long a city of empty Victorian churches. These Gothic chapels now echo to Polish mass and Nigerian choirs. Polish churches are full of toddlers and pushchairs. Teary tattooed plumbers cross themselves. Hard-up meat packers shove £20 into the collection boxes for the nuns needing furniture in eastern Poland.

I went drinking with Miner. We began in the newsagent by filling a blue plastic bag with a dozen cans of Lechs. It tore. Traipsing home, Miner shared his confusion about the English. "Why do they give the benefits? Why £60 a week and a free flat for a lazy pig that don't work?"

Miner snatched the police notice in his letterbox. "Fuck, not again." He quivered in rage. "The black people are at it again!" Miner lived in that part of London derided as Poundland. Dirty parades of betting shops, twirling doner kebabs, payday lenders, unlicensed pawnbrokers and signs for "We Buy Gold". The cans were cracked open. Miner drank and grew flushed. There were six people living in two rooms. My friend, his girlfriend, and his father in one room. In the other, Margarita the cleaner, her boyfriend and her tired mother.

Polish builders are a little bit racist. London is probably home to more than 300,000 Polish migrants. But we can only estimate that. So keen are they to save that little bit extra that many go under the radar to avoid tax. This is why every builder I spoke to on the site had been burgled. Their flats are always the cheapest, built with flimsy locks that can be undone in 10 seconds. Sometimes landlords are in on the racket.

Burglars love Poles because they are paid in cash and hide it in shoeboxes. When they see builders and cleaners moving in over the road, they are already laughing. They can sometimes make £5,000 from one bedsit. And they know the Poles will never call the police.

Miner wanted to relax by showing me pictures of £5m townhouses he had renovated. I was saved from this melancholy slide show by the return of Margarita the cleaner. Like all cleaners, this girl from Bialystok likes to boast she knows everything about her homeowners. "I could hold them to ransom." She giggled. "I know the Clapham housewife who cheats because I clean the sheets. I know the Clerkenwell banker who loves cocaine because I find his powdered Oyster card."

But cleaners never think of themselves as cleaners. They are always future professionals. They have big dreams about Britain, unlike their boyfriends, because they speak English. English unlocks London. Before long, many start flirting with the charming boys working at JD Sports. Those in love with Polish men start to tell them they want to have children here.

Miner's eyes revolved. This is how the Polish dream house slips out of sight. His girlfriend wants to stay. London has left its Polish builders feeling emasculated. A labourer earns £7 an hour but a cleaner makes £10 an hour. Workmen unable to speak English have little choice but to chase Polish girls they cannot afford the cocktails for.

Not everyone will get lucky like Miner. In 20 years, he will still be here, probably in Streatham. He will have a cocky son with literary or financial aspirations in a sixth-form college, flaunting a fashionable Polishness.

The luckless in Polish London drink. Drinking blights the Polish countryside. This has now come to the streets of London. The majority of tramps in the city are Polish and Lithuanian. There are at least 5,000 of them. Over 3,000 have been bussed home over the past five years.

There were Polish tramps in north London who were forced to work unloading trucks for Turkish shopkeepers. These villains paid them in the tramp's drink of choice – White Ace cider. I cannot describe how bad it tastes. Others were found roasting rats in back alleys in Tottenham and Haringey.

These humiliated tramps are hiding. They are hiding from their families. Unable to bear the shame that London turned out to be a soiled mattress under a flyover.

Every year, there is a service at St Martin-in-the-Fields for those who died on the streets of London. They are men who were run over by minicabs that never stopped. Men who fell asleep on the Thames shore at low tide but could not swim. Most of them were Eastern European tramps.

The artful dodgers of this London are the Albanians. They are the only people the Poles are afraid of. Builders tell stories of Poles who went to work for Albanians only to be beaten into a coma when they asked for their wages. They ask how Britain could ever have let such dangerous people in.

The Albanian pub in Kilburn looks like a normal pub, your classic dingy mock-Tudor watering-hole. But outside they are grilling meat just like in the Balkans. Guys in gold chains and holed fashion jeans sit outside smoking with cute girls in fake fur collars. The Albanian pubs are full of mafia stories. This is because the Kray brothers of today are from the Balkans. The Yugoslav wars brought at least 30,000 Kosovar refugees and Albanian runaways to London. The wave brought with it several hundred gangsters, hardened KLA veterans and sworn brothers from criminal mountain clans.

Albanian London despises the mafia. Pints are raised to their downfall in Kilburn pubs. These are honest people furious that criminals have tarred their name. These people love Britain more than Ukip ever could. This is because Albanian London is one of refugees. Fathers named daughters born in the UK after sisters tortured by Serbian paramilitaries in Kosovo. Children are taught about Tony Blair granting them asylum which saved them from war and poverty.

Poles and Albanians talk about Britain as a "mini-America". But there is no British dream. East Europeans came to London not inspired by a dream of how great things could be, but by the knowledge of how much worse they can be. Talk of Britishness draws a blank face. Immigrants say, "Britain is a land of opportunity". But they do not feel particularly welcome. As if they are living in a spare room.

A longer version of this article is published in the November issue of Standpoint magazine, standpointmag.co.uk/node/5252