Naturalisation. Good character. Criminality. Persistent offender
If you apply to naturalise as a British citizen, you must satisfy the good character requirement. A factor considered when assessing your character is whether you are a persistent offender.
If you committed more than one (even minor) offences in a short period of time, you may be classed as a persistent offender. It depends, of course, how many offences you committed and in what period of time, and whether the offences have been serious and impacted the public.
The offences may have been committed in the UK or abroad.
The Home Office guidance on the good character requirement gives an example and makes the distinction between a non-persistent offender who has committed 4 minor offences in 10 years and a persistent offender who has committed 3 offences in just 6 months.
If you are a persistent offender, you will fail to satisfy the good character requirement, and your application for citizenship will be refused.
If you want to apply for British citizenship or for a British passport and need specialist advice, feel free to contact me. Please note that I am an accredited immigration adviser, not an employee of the UK Visas and Immigration. I charge fees for the advice provided.