Naturalisation. Good character. Criminality. Convictions outside of the UK
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 have overseas criminal conviction or non-custodial sentences.
If you have committed an offence abroad and you have received a custodial or non-custodial sentence, you must admit that and declare it in your application for citizenship. You may not satisfy the good character requirement and have your application refused, but it is still better than making false or misleading statements regarding your criminal history, in which case you may be using deception, which is an additional ground of refusal.
The Home Office may anyway find out about your convictions from other sources.
If you have committed abroad an offence which is not classed as an offence under UK law (for example, if you have been convicted for being homosexual, or a member of a political party or of a trade union), it will probably be disregarded during the assessment of your character, unless it counts as an evidence of your willingness to disobey the law.
Each case will be decided on its own merits.
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.