S21 expired notice

Tenancy Types and Management

I served a section 21 on the same day as the AST (on the day the tenant moved in - tenant signed). The tenancy is now periodic and the S21 has technically expired. If I now want to reclaim the property, how much notice do I need to give? In theory none, as the statutory two months was covered in the period of the tenancy, but I'm sure the courts would take a dim view of that should the tenant not leave and I have to resort to court proceedings!
Do I need to issue a letter asking for possession giving a certain date for vacation? How would you approach it?
TIA

Martyn Nicholls