Hi Alex,
I think I understand what your question is about (but please correct me if I am mistaken). Phrased differently, "If I want to increase my rents, will the (proposed) removal of S21 make it more difficult to do so?"
In your example, the length of the fixed term, and/or the proposed refurbishment make no difference to your situation: you want to increase the rent and are worried about a backlash from the incumbent tenant. Let's unpack your scenario:
At the end of a fixed-term agreement you are able to increase rents as you wish - this creates a new AST under your new terms