The English National Archives has announced a collection of 7,000 naturalisation records about foreigners who settled in Britain and who became British citizens through the process of naturalisation. Although there are some records for the period 1801 to 1843, the bulk of the records date from 1844 to 1871; 1844 being the date of the Naturalisation Act which required foreigners residing in Great Britain with intent to settle to send a memorial to the Secretary of State stating their age, trade and duration of residence. There's an example image of a memorial for Paul Julius Reuter , a guide to naturalisation and British citizenship and a lot more on their blog.
Information on these records may provide nationality, occupation, family details, date and place of birth, year arrived in Britain, address, character references.
I haven't found any ancestors or family members in the records but that's probably because they immigrated in the 18th or 20th centuries.
Search the 19th century immigrant naturalisation records for yourself.