I can't speak for the railways, but have had some involvement in this (taxi licensing) sort of thing
I would not have thought that this job would be a full scale DBS check, so any convictions that are legally 'spent' would not be relevant. Full scale DBS (including spent convictions) can only be put through where the job is particularly sensitive (mainly jobs involving working closely with children and / or vulnerable adults - think there are a few others) - an employer can't do full DBS on anyone or everyone just because they feel like it.
A full DBS can include information about arrests (and then only where someone's had a few arrests for sexual offences - now's not the place to argue the merits of this, but look up the Soham murders case)
But I am fairly sure that a basic disclosure (which is what I assume is going to be relevant here) does not include anything other than convictions - an arrest or charge that didn't end up with a guilty verdict won't show up.
This page (NACRO) is another that has more about spent convictions - how soon an offence becomes spent is on a sliding scale based on what the sentence was, rather than what offence it was. (May be worth talking to NACRO as well)
Apart from jobs involving access to children etc and people who have got a record in that sort of direction, DBS's role is not to say to an employer "no, you can not employ this person" - they will provide the relevant info and it's up to the (potential) employer to make a decision.
Some organisations will be reluctant to take what they see as a risk in employing anyone with any sort of 'record'.
Larger organisations should have a policy, and will make decisions case by case. All I can find on LM is
this page - includes " If you have any concerns in this area we do ask you to make us aware during the application process so that we can undertake a fair review"
If you've so far not been asked to declare, I can see the difficulty in that you might not want to rock the boat and risk losing the agency work as well.
What I would say is that if you do go through with the application, and you're asked to declare (within the realms of unspent convictions) then best approach is to tell the truth.
Employers who may be prepared to give someone a chance (possibly after a chat in which they may be looking for you to explain how you've reformed and so on) tend to be less understanding if they think someone has lied to them - it can even lead to being sacked after you've started if they find out later that something in your job application was untrue.