It is often easier to blame others (immigrants in this case) than look at what you are doing wrong or where you could improve. Britain is more likely to fail in a globalised economy, and not because of cheap labour or immigration, but mostly because of flaws in the education system and styles of parenting.
While visiting British state schools I have noticed that children are given less homework than their peers in European countries (where children would normally spend 2 to 3 hours a day doing homework).
Another big problem is the way that languages are taught in this country. Children are mostly taught basic phrases that they would need if they went on holiday to France, Spain or Germany, but with that amount of second/third language they would struggle to work in a job where multiple languages are needed (this is a requirement for more and more jobs, as companies open multiple offices around the globe). Today I've seen a mother on MN complaining about her four year old learning too much French at an English school. That, I can not comprehend.
Third big problem lies within teachers' inability to interest children in science, maths, IT, geography and history. Instead of encouraging children to be scientists, IT programmers, doctors, lawyers, dentists, economists, historians, politicians, children are encouraged to be creative and artsy and dream about being in a media business or doing Gaga degrees.
There is also a lack of imposition of a hard working culture to children from a young age. What you call "pushy parenting", we call "parenting". Children not only do lots of homework, compete in olympiads, but often (up to 5 times a week) attend art, music, sport school, where they have to do extra homework, take exams yearly and are expected to give performances and attend competitions. I find that in Britain there is this fear of criticising children (we all probably heard about children getting medals even if thy came last).