Almost three-quarters of employers say implementing the new points-based system (PBS) had increased their administration costs, a survey has revealed.
The December Immigration Survey, by Sarah Buttler Associates, also found nearly 40% of respondents who have registered to sponsor migrant workers have been forced to wait more than four weeks for a response to their applications, and have consequently struggled to hire or transfer migrant workers.
Four in five employers were against a US-style cap/quota system limiting the number of migrant workers.
Around 70 companies employing more than a total of two million people took part in the survey.
Home secretary Jacqui Smith said British people will have the "first crack of the whip" of jobs classified under Tier 2, which includes primary school teachers, construction jobs, some nursing categories and hotel managers.
"When it comes to immigration, in difficult economic times I believe we need a tough system that offers British workers the first crack of the whip for British jobs," said Smith.
"That's why I'll be using the flexibility that the points-based system allows to force employers to offer British jobs through Job Centre Plus before recruiting foreign workers," she added.
Currently, employers must advertise a job nationally for two weeks before looking for workers from overseas. The time limit drops to one week where a salary of more than £40,000 is on offer.