I’m afraid that ignorance of the law is no defence. You didn’t protect the tenants deposit in a recognised scheme and hence, the tenant can claim to 3 times the deposit from you as compensation if he decides to take you to court.
You cannot use the section 8 or section 21 procedure to get rid of him because you have failed to comply with your statutory obligations in respect of the deposit. It would need a bespoke court application to get him out.
You now need to protect the deposit in a recognised scheme and give him the details. Then you can use the section 21 and section 8 process to get him out .
Even then, and even after he leaves the property, he can still bring the claim for three times the deposit from you.
It potentially gets worse and if the tenancy has ever been renewed or rolled over into a periodic tenancy, each of those renewals is a further breach. Hence, if the initial term was for 6 months and he does just rolled over since, you are potentially at risk for six times the deposit to him. The courts will not routinely award six times the deposit that is the problem that you potentially face.
Many solicitors are now actively looking for this kind of work and trying to find tenants whose deposit has not been protected, with a view to suing the landlord. They will do these on a no win no fee basis because there is no defence the landlord can put forward.