As you are aware, if you do nothing then a periodic tenancy will arise. In such a case they are unable to levy a charge (they can try but will have no means to enforce it) and your tenancy will continue on a month by month basis (assuming you pay rent monthly). Of course, this means that your LL can issue you with 2 months notice to leave.
Will they? If what you say about being a good T is true then it is unlikely that a rational LL would chose to evict over allowing a periodic tenancy to arise unless the agent accidentally on purpose mis-advises them in their quest for fees. To counter this, it would be a good idea to write to your LL explaining that you wish to stay on a periodic basis (and you can also complain about the agent). If you don't have the LL's address then you should write a letter to the agents asking them to provide the name and address of your LL as required under S1 of the LL and T act 1985. They have 21 days to provide the address and will presumably remind them that you mean business.