That's a fallacy and you know it. I am not excusing Blair, but defending employers who recruit foreigners.We could have got ALL the jobs filled by white Europeans
Most jobs taken by Chinese, Bengla Deshi, Poles, Latvians and others are systematically turned down by white Brits. I have witnessed it several times.
A friend of mine in Lincolnshire had to obtain permission from the Ministry of Agriculture, Fisheris and Food, to recruit abroad because he couldn't find worker in his area to fill farming and food producing jobs. His job offer adverts were ignored in a region of unemployement and he finally contracted Ukrainian seasonal workers to fill up vacancies - all with the ministry's approval. His rate of pay were well above the minimal wage, he provided FREE lodging and food to. Not one local applied!
I have also heard from restaurateurs in London that mostly foreigners answer job offers for waitress, kitchen portes, bar staff, etc... Most of these jobs could be taken by Brits.
There are plenty of unemployed Brits who don't look for work and prefer to stay on benefits. That's the sad truth. Blaming foreigners for their willingness to get on the job ladder has become a national sport in UK.