Members of the EU, EEA and of Switzerland do not need a work permit. The UK Border Agency monitors work visas and provides specific information.
To apply for a student visa, you may apply for a Tier 4 Adult Visa (age 18 or over) or Child Visa (between ages 4 and 17). This visa is to enroll in a degree program or other long-term course of study.
If your spouse, partner, parent, grandparent or other eligible family member is a citizen or permanent resident of the UK, EEA or Switzerland, you may be eligible to apply for an EEA Family Permit. You may submit your application for the EEA Family Permit to enter the UK along with your family member or you may apply to join a family member who is already in the UK.
The UK and Ireland have opted out of the Schengen Agreement. The UK wants to maintain its own borders, and Ireland prefers to preserve its free movement arrangement with the UK, called the Common Travel Area. However, they do participate in some aspects of the Schengen agreement, such as the Schengen Information System (SIS).