European nationals have the rights to move freely in the UK under the free movment principles of the European regulations. Under European regulations, 2006 (EEA Reg), European nationals have the rights of entry to the UK just as much as British citizens have rights to enter other European countries. THis is called the initial rights of residence. In that period however, it is expected that they are excercising treaty rights. A way to prove this is through a registration certificate. Note that this is not really important.
EU nationals and their family members have the right to remain and work in the United Kingdom.
The following are the various applications required by the EEA nationals and their family members to make available to the Home Office, UK Visas and Immigration: