Hi, thanks for your question. My names Vincent and I'm going to help you with it.
If you allow your current tenancy to come to an end (presumably, in this case, you served notice on your landlady) and your landlady decides to rent the property to you without using the lettings agency for "rent collection" or "property management" (whichever the case is here), the likelihood is that she will be the only one risking a possible breach of contract with the agent, not you.
The reason she might be in breach is because some agreements entered into between agencies and landlords require "renewal fees" where the contract is renewed on a fixed term to the same tenant. This is an unusual scenario and it would depend on the wording of the agreement between your landlady and her agent whether or not the clause operated in these circumstances. However, I'm sure that a correctly worded agreement would include something for revenue protection purposes and to stop otherwise blatant avoidance of agency fees. However, as I say, that is between her and the agent.
I doubt that you will have signed anything with the agent that would prevent you from doing this but you should just doublecheck your paperwork for peace of mind.
Does this answer your question. If so, please don't forget to rate my answer so that I can obtain credit for my work. Our conversation, won't end and you can ask me any further questions you need to clarify the above.