If you are a non-EEA national you must have permission to remain here in accordance with the UK's point-based immigration system.
Most international students will need to apply under Tier 2 General in order to work in the UK after the end of their course
What is Tier 2?
Now that Post Study Work (PSW) is closed, Tier 2 is the best option for most students hoping to work in the UK after their studies. Tier 2 is part of the Points Based Immigration System and is for skilled migrants with a job offer. You can apply for an employer sponsored work visa under Tier 2 if you have a job offer from an employer who is on the Sponsor Register of Employers and are issued with a valid certificate of sponsorship. See the link below: http://www.ukba.homeoffice.gov.uk
The Home Office introduced lower "new entrants" wages on 6th April 2013 for Tier 2 (General). This is for recent graduates switching from a Tier 4 Student visa to a Tier 2 General visa who meet the post study work provisions as outlined above. For example, a new entrant Financial Manager will be expected to earn at least £25,600 rather than the normal salary of £37,500 and a new entrant Business Analyst will be expected to earn at least £24,900 rather than the normal salary of £30,600. The salaries are listed on the codes of practice, available here. http://www.ukba.homeoffice.gov.uk
You have to apply for the visa with the sponsorship certificate and you need to pass the points-based assessment including a minimum salary for the post.
You can use the points calculator on the UKBA website to check if you meet the points requirement. http://www.ukba.homeoffice.gov.uk/pointscalculator