To work in the UK you are required to be a UK citizen, or an EC/EEA national. Commonwealth citizens and foreign nationals with no restrictions on their stay in the UK may also work subject to visa restrictions/status.
Husbands, wives and dependent children of people who hold a work permit or certificate of sponsorship may be permitted to work as long as their visa/biometrics card places no restriction on employment in the UK.
If you do not meet any of these criterion, then you will require a Certificate of Sponsorship or authorisation from the UKBA e.g. Tier 1, international student visa in order to take employment.
For some job vacancies requiring specific skills we may consider issuing a Tier 2 Certificate of Sponsorship if you are suitably qualified (provided a Resident Labour Market test has been carried out and no suitable settled worker can be appointed) as part of the process of obtaining permission to work in the UK from the UK Border Agency (UKBA).
Normally, Tier 2 sponsorship will normally only be offered for academic and research roles.
You can check whether you would be eligible to work in the UK under the points-based system for migrant workers using the UKBA points calculator.