In my experience most contracts require you to confirm that the director and/or representative doesn't have any unspent convictions. It's of course up to him whether he wants to lie and deal with potential consequences. In practice there are very little checks though.
I'm a freelancer/contracter in the UK working through my own limited company. Most of the time I try to use my own contract, but if clients insist on using their own, I will sometimes use them.
I've gone through a few of those where the client supplied the contract and only two out of maybe a dozen had any caluse related to convictions (from a quick search of them).
One was a clause about people working on the project being:
> fit and proper persons for the tasks assigned to them, and in particular have no unspent criminal convictions for any offence involving dishonesty or computer crime
Another had a clause about terminating the contract early if the contractor is:
> being convicted of any criminal offence other than a minor driving offence under the Road Traffic Acts
None of the others I looked at had anything else like that. I don't think any convictions would be a major barrier for OP if they are working with typical private sector companies. As other have said, it's likely any public sector work or specific industires such as education, defenece, or finance might have more checks in place.
Many convicted white collar criminals are barred from being a director of any company. Using a company for money laundering would be a good basic example.
This kind of thinking is what got him in to this position in first place. There's a reason convicted money launderers shouldn't be allowed to run companies.