If you are an EEA or Swiss national and you are exercising Treaty rights in the UK, then you may apply for a registration certificate which would confirm your rights of residence in the UK.
EEA nationals include citizens of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland | France, Germany, Greece, Hungary, Iceland, Irish Republic, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden and United Kingdom (including Gibraltar).
EEA and Swiss nationals have the right to enter the UK and live here for 3 months. If you wish to stay here longer than 3 months, you must become a “qualified person”.
However, the registration certificate does not qualify you for British citizenship.