Old political hands used to say that in parts of the country you could stick a red or a blue rosette on a donkey and they’d still be voted in, so fierce was the loyalty to the Tory and Labour parties. Looking at some who have adorned the green benches in the House of Commons, it’s obvious the major parties have proved the old saw correct.

These days it’s not so simple. When my parents arrived from the Caribbean in 1950, more than nine out of 10 Britons voted either Labour or Conservative. In 2010 that number had fallen to seven in 10. The missing votes are leaking to Ukip, surging against the Tories in the east of England, to the Greens in the South and West, and to the SNP in Scotland.

But here in London, where smaller parties still don’t do so well, the big parties’ bosses have a different headache. In the capital, if you want to predict the outcome of the next election, don’t bother to check the colour of the rosette. Look instead at the colour of the voters’ faces — it’s a far better guide.

The Conservative peer and pollster Lord Ashcroft reported last year that being non-white is now the best indicator that someone won’t vote Tory. Analysis of the May 2014 European elections by my colleague Professor Richard Webber of King’s College and I showed that two out of every three non-white voters in London plumped for Labour. Two out of every three white electors chose either the Tories or Ukip. And in the local council elections some unexpected results can only really be explained by the extraordinary rise of ethnic-minority influence.

Labour claimed advances in many formerly true-blue Tory councils such as Merton and Croydon. The borough of Redbridge, for example, has given the world Iain Duncan Smith, Norman Tebbit and, further back, Sir Winston Churchill, yet chose the red team. Our analysis suggests that it’s the minority dispersal into London’s middle-ring suburbs that is turning former Tory marginals such as these into Labour strongholds.

The increases in ethnic-minority shares of the population in the past 10 years are spectacular: Croydon up 50 per cent, Redbridge up 32 per cent, and Harrow now more than 60 per cent ethnic minority, and home to many affluent but Labour-loyal Indian voters. Labour’s “surprise” victory in Hammersmith and Fulham looks far less surprising in the light of dramatic demographic change. The visible minority share of the population in the borough is up by 45 per cent, from 20.2 per cent to 29.3 per cent — an increase of nearly half.

Non-white Londoners are already nearly as numerous as white British Londoners, and set to overtake them within two elections’ time. It’s not hard to see the direction of travel. The Conservatives know that their history counts against them. It’s not just the legacy of Enoch Powell; most ethnic minority voters simply think the Conservative Party doesn’t like them.

Our work also shows that the less integrated a minority group is, the less likely they are to throw off that historic anti-Tory prejudice. Recent work from the Social Integration Commission shows that contrary to our self-image as happily multicultural, Londoners are the least likely people in the country to mix socially with people outside their own ethnic group. And with more than 600,000 white Britons moving out of the capital in the past 10 years, the opportunities for day-to-day integration are dwindling.

These numbers explain the extraordinary persistence of an eight-point Labour lead in the capital, according to one poll this week, completely against the grain of what is happening elsewhere. If Tory strategists can’t break this pattern, they can kiss goodbye to a Conservative Party ever again ruling Britain alone.

That may explain why late last year, the Conservatives organised a visit to London by Canadian Defence Minister Jason Kenney. He is also the Canadian Tories’ Secretary of State for Multiculturalism, charged with tackling a problem remarkably similar to the one facing Cameron. And he has worked a minor miracle for the Canadian Tories.

Almost half of Toronto residents are “visible minorities”. The Tories should have no hope in that city. Yet in the 2011 Canadian election, they boosted their tally of seats there from 14 to 31, while the Liberals (Labour’s nearest equivalent) plummeted from 32 to seven.

Kenney, known widely as the Minister for a Curry in a Hurry, has worked tirelessly to make minorities love the Tories. He turns up at hundreds of ethnic events every year, sometimes reputedly inviting himself. No religious or ethnic festival passes without a congratulatory card, a flurry of tweets, plus a visit to the temple, gurdwara or pagoda. He created a new centre for religious freedom. And he made sure his party looked different. Today there are 12 minority Tories in the Canadian Parliament, their highest-ever number.

Kenney didn’t stop at love-bombing immigrants. He attacked the opposition for taking minority voters for granted, accusing them of “mailing it in” during the election campaign. Labour’s energetic London supremo Sadiq Khan MP would never be guilty of complacency. But Labour should pay attention to the numbers too.

First, in last year’s Euro elections, Labour took just 10 per cent of the white vote — and were outpolled by Ukip by almost two to one. Second, minority voters are looking elsewhere. In 1997, 77 per cent of Indian voters — London’s largest minority group — identified with Labour. Of the second-largest group, African Londoners, 79 per cent claimed to be Labour-loyal. Today those numbers have crashed to 45 per cent and 59 per cent respectively.

Labour’s determination to hold its vital ethnic edge will soon be tested. London elects its next Mayor in 2016. Margaret Hodge, MP for Barking, recently attracted controversy by suggesting that Labour should be looking for a great minority candidate to carry its colours, if not this time, in 2020. The arithmetic says she’s right. It’s a message the Conservatives need to heed too.

Trevor Phillips is chairman of Green Park Diversity Analytics.