Many thanks for your patience, I am pleased to be able to continue assisting with your query now.
You can find the relevant guidance on this here:
(Scroll to 2.5)
Specifically, it states:
Before reaching a decision on whether you’re a ‘fit and proper’ person, the risk you’re likely to pose to pupils is assessed by considering factors like:
whether the caution, conviction or other information revealed is relevant to the ADI role
the seriousness of any offence
the circumstances surrounding an offence and the explanation
the length of time since the offence occurred and if it’s ‘spent’ under the Rehabilitation of Offenders Act 1974
whether there’s a pattern of offending behaviour
whether the circumstances have changed since the offending behaviour
Each case is considered on an individual basis. The ADI Registrar will write to you giving you the opportunity to explain your circumstances before making a final decision.
It then also goes on to say:
You’re unlikely to be ‘fit and proper’ if you’ve been cautioned for or convicted of: possession or supply of drugs.
So I am afraid there is no definitive answer to your query. They will likely see the history of your criminal record and make a decision based on it but just because you have that history does not automatically mean that you will be considered unsuitable for the role. It could be that based on the time that has passed and the minor nature of the penalties, that they would consider this no longer relevant, but you won’t know until you have applied.