I do not believe there is legislation or powers with the FCA to control rates, although contract law with particular reference to fairness is often cited. However, there is at least a position on how to manage SVR customers and on the whole, appear to be more onthe side of the consumer.
The "Dear CEO" letter from 2013 references the principles of fairness in dealing with customers:
There is also an interesting discussion paper from mid 2014, I cannot see if the responses have resulted in a policy change as yet but maybe some other posters can turn up something.
A case study example in the discussion paper outlines how the FCA expect a bank to conduct itself when changing the SVR. Transparency and justification based on concrete evidence i.e. increase in funding costs or deposit interest are cited as being a fair reason.
Irish Banks, until the recent attention on the subject did not provide such justification or transparency, other than grunting about arrears or trackers or wanting to return to profitability. Their lack of unity on the matter has eroded their credibility. I'm a customer of Ulsterbank, I wonder can I complain to the FCA!