Yasmin Alibhai-Brown: If you don't want immigrants, will you then do their jobs?

Our instinct for survival makes us push the work ethic into our kids

I have long had this fantasy. With millions of true-born Brits reviling immigrants and blaming incomers for everything – unemployment, poor public services, crime, violence, social unease, widespread rape even – why not have an annual day called "Immigrants Out".

We who are thus pilloried, and our progeny, previous arrivals and their descendents too, should put down tools, shut up shop and march in our best clothes to show the many unappreciative citizens just what we do. We could pick the birthday of Mary Seacole, the Jamaican who nursed our soldiers in the Crimean War.

Mayor Boris Johnson should fund this carnival. It would make better sense than his proposed day to suck up to America. After all he supports an amnesty for migrants.

In all the hysterical, anti-immigration debates a question hangs like an eagle looking down from the clouds above. What would happen if the immigrants left?

At long last a media experiment tries to tease out some answers and you can watch the results at 9pm this Wednesday on BBC1. The presenter is Evan Davis, one of the interrogators on the Today programme. The programme is set in Wisbech near Peterborough, once a prosperous English town which has attracted over 9,000 workers from central and eastern Europe who do factory and field jobs.

Over 2,000 locals are unemployed. They are none too happy. The place they say is "overrun with the buggers" and "they're pushing the English person to one side". Meanwhile employers claim they had to turn to migrant labour because they couldn't get good indigenous employees.

So the BBC took out a dozen foreign workers and replaced them with unemployed Brits looking for a fair chance. Jobs were made available in a factory, an asparagus farm, a building company and an Indian restaurant.

Half the British workers either failed to show up or turned up late on the first day. Thereafter, the tasks proved to be beyond the endurance of most of them. I sympathised with them initially – especially with Terry and Paul, mates who used to repair water mains, and Terry's wife who wept as she described how she feared they could lose their home. Paul, a single father, was learning maths from his 11-year-old daughter. It didn't seem fair, their suffering.

I wanted them to do well but couldn't stand the self-pity and anti-migrant bitterness. Paul refused to call his co-worker by his Portuguese name, he wouldn't respect a "foreign" supervisor. In the end they did shape up thanks to a feisty, young female English manager who didn't put up with their rubbish.

A resentful builder also started off badly but came right. But most of the rest failed miserably even with kind bosses. A chef at the Indian restaurant given the job of taking orders didn't survive a single morning. The owner graciously invited him to have a meal before leaving. The youngest lads were the most useless. My English husband couldn't bear to see what the working classes had become – his own class in fact.

All the businessmen said they would like to provide jobs for the community – it just wasn't possible. They denied they were trying to keep wages down.

Pressure on services was also explored. It is indisputable that the new populations are adding demand to hard-pressed authorities. Yet one school head insisted: "Nobody suffers, everybody gains", possibly overstating the good news. But witnessing "British jobs for British workers" in one small part of the country you understood how the services too would collapse without migrants.

Political parties now battling it out over the needs of the old will never be able to provide quality care for an ageing population using only homebred staff. There are, no doubt, hardworking Brits across the land – like the manager at the potato factory – but too many who will not get out of bed for love or money or a job. I know a number of lazy good for nothing migrants too. However, most of us immigrants feel insecure and vulnerable and can never take anything for granted. The survival instinct makes us push the work ethic into our kids.

I have been helping out occasionally at the café in the crypt of Marylebone parish church run by a chef, David Rowles, with whom I am trying to set up a small cookery business. I wash up and serve customers at the table. When I get things wrong Rowles gets mad. That's fine; I am learning. One customer recognised me and was shocked. How could someone like me be doing this? I'm an immigrant I explained. We never think we are too posh for any job. She smiled and left a good tip.