If we fail to help such people integrate into our society, then we are creating problems for the future. In years to come, young people who have grown up here feeling rejection, animosity and isolation will be angry and resentful. They will have underachieved at school and will end up unable to contribute positively to our society. I fear we have not learned the lessons of the past and that we are continuing to create many young people who feel excluded from society.
Growing up in Trinidad in the 1950s, I felt very much part of the British Empire. We were taught about Britain, its heroes and its history, sang the National Anthem and Land of Hope and Glory, and on Remembrance Day we wore our red poppies with pride.
It never occurred to us that we were being taught nothing about our own history or culture - we just accepted that we were British. Ironically, those early lessons stood me in good stead. In 1960, when I arrived in England to start a new life, I already knew much about my new home, its customs, people, geography and language. Sadly, at my first English school I was amazed to discover neither the teachers nor the pupils knew anything about where I came from or why I had ended up in their classroom. It was quite disorientating, undermining my self-confidence and almost making me feel unimportant as a person.
Children from Caribbean islands as different as France is from Finland were lumped together as "West Indians" by teachers who knew nothing of our customs, accents, food, culture or history. We were treated badly and endured tremendous ignorance and racism.
One teacher told me I did not need to learn to swim because I had an extra bone in my foot. Some children asked to see my tail and touched my skin to see if the colour would come off. Perhaps if the then government policy of encouraging West Indians to come to Britain to help rebuild after the war had included a public awareness campaign to teach the British population more about us and why we were arriving, there would have been far less animosity and racism and we would not be suffering the repercussions of it.
Since Roman times, Britain has been a place to which people have migrated. Over the centuries their culture and language have blended with this country's. Unfortunately, it is taking longer for Caribbean, African and Asian cultures to merge because of colour, which is still seen before the person.
Now we are experiencing an influx of asylum-seekers from Eastern Europe, yet we know little of their culture and customs. I am afraid that if we are not careful we could fall into the same old trap of allowing their children to become isolated.
Parents of such children may decide to form their own schools, which in the long term makes the problem worse. I have always maintained that schools catering for children with the same religious beliefs and cultures do not break down barriers, they build them.
Far better that teachers are given guidance and information by a government which helps pupils to develop understanding and awareness of other cultures.
Certain responsibilities lie with those who have decided to make their home here, of course. I remember being told by my English teacher to speak the Queen's English if I wanted to remain in her class. At the time it seemed harsh, but in fact she did me a big favour. I was able to make myself understood and break down the barriers caused by my accent. Now I can easily switch between my lyrical Trinidadian accent and my straight English one - very useful for someone in my business.
Integration does not mean giving up one's identity - it means widening one's understanding of cultures in order to live together in a harmonious and happy society. Migrants all have a gift of some kind, something which culturally will enrich our lives. Let us not slam the door in the face of diversity but embrace it with respect, for the sake of all our futures.
Floella Benjamin is a broadcaster, writer and independent TV producer. Her latest production, 'Coming to England', a BBC Education series, has just ended its run on BBC2.