Can Company Let roll into a Periodic tenancy ?

Tenancy Types and Management

Hi. we have a company let and the tenant wants to extend by 1 month before comitting to a formal renewal. The tenancy agreement talks about extenstions and continuations but makes no specific mention of how this should be documented. My question - should we draw up a short addendum to confirm this arrangement or would the fact they had paid an additional month's rent qualify as confirmation the tenancy has rolled on for a month on a periodic basis? I am consious this is a contractural tenancy with non of the Housing Act legistion applying. Thank you in adavance !