UK residence permits are issued by the Immigration and Nationality Directorate (IND) part of the Home Office. These principally affect non-visa nationals who intend to extend their stay in the UK beyond six months.
EU/EEA nationals do not require residence permits. However, if you wish for non-EEA national members of your family to join you in the EEA UK, you will need to apply for an EEA Family Permit. You can only apply for a Family Permit in the country of which you are a national.
On arrival in the UK, you will be given an entry stamp to the UK for 6 months. If you wish to extend your stay, you will need to apply to the IND for a residence permit. Note that the IND will charge a fee for this.
Further information on residence permits, including downloadable application forms, can be found on the IND’s website www.ind.homeoffice.gov.uk.