You are not necessarily prohibited from applying if you have any form of a criminal conviction. It really will be a case-by-case assessment by your legal practitioner or by your advisor or by the minister themselves in determining how that’s disclosed and how it’s dealt with.
What is most important is that you fully disclose those criminal convictions and that we would advise doing a Subject Access Request to ensure that you have given the minister the full picture and that you’ve provided as full of an explanation as possible to show why you are still of good character notwithstanding the criminal conviction itself.