UK law permits multiple citizenships and there is no requirement to renounce previous nationalities, as dual citizenship is allowed in the UK. It is however worth checking the national laws of the other country you are looking to continue or holding the nationality as they may have a different criteria.
It is possible to apply for resumption of British Citizenship if anyone has previously surrendered their nationality. However it may be possible only if renunciation was necessary to enable the applicant to retain or acquire some other nationality.
There is no statutory definition of good character and no statutory guidance on the interpretation or application of the requirement. The Home office internal guidance for caseworkers states that a person may be considered to be not of good character if they have a criminal conviction, used deception in previous immigration applications or filed for bankruptcy or had unlawful recourse to public funds.
British nationality applications are decided by the Home Office normally within six months. Applicants will need to attend a Citizenship Ceremony to receive the Naturalisation certificate and then apply for a British passport.
Application needs to be certified by two referees, each of them has known the applicant for at least 3 years, has no criminal convictions within the last 10 years and is not related to the applicant or to each other. One must be a person of professional standing and the other person must be over 25 years old and hold a British Passport.