Tenant leving

Possession - Section 8 and Section 21

We have inherited a property from another agent with a tenant in significant rent arrears - about 6 months. The previous agent had not registered the deposit.
We were granted possession under Section 21 but the tenant appealed and possession was overturned because of the deposit issue.
The landlady would be willing to let the arrears drop if the tenant agrees to leave the property by an agreed date -from her point of view the sooner the better.
My concern is that if we strike up a written agreement with the tenant and the tenant does not leave then we are stuck with him.
Are there any implications re: Housing Act etc. that we need to be aware of in striking up such an agreement?
Given the possession has been overturned what course of action would you suggest re: eviction? If we went under Section 8 would the lack of a registered deposit still be a barrier to securing possession?

Thanks in anticipation.