If your ancestors came to Britain from abroad, they may have settled and sought British citizenship, which will have left useful records.
Britain has seen many waves of settlers over the centuries, but before the Regulation of Aliens act of 1793, there were no precise controls on immigration. The Act obliged aliens to be recorded on entering the country and to need documentation if they were to travel beyond their port of arrival. Few of these records survive, but when people wanted to become British citizens, a paper trail was generally left which remains today.
Before 1844, there were two routes to citizenship. One was naturalisation, which required a private Act of Parliament (and for the person to take Anglican communion). This was expensive but granted all the rights of a natural born citizen.
Denization was simpler and cheaper - the term refers to 'letters patent' granted by the Crown. Letters of Denization could have restrictions applied - typically that the subject would have to pay double taxes and could not inherit property. Records of both kinds can be found as far back as the 16th century.
After 1844, the process was simplified, and the Home Office began granting certificates - the case papers for these are held at the National Archives. After 1948, the government introduced more straightforward nationality certificates.
Many records up to 1800 were published by The Huguenot Society. Records from the 19th Century onwards are generally at The National Archives, and now TheGenealogist.co.uk is putting up a wide range of denizations and naturalisations online, including Acts of Parliament, returns of naturalisation of aliens and denizenship applications by letters patent.
Find Home Office naturalisations at TheGenealogist