David Davis has confirmed we will diverge from EU regulations after Brexit (HERE). Of course, we will be free to do as we wish after Brexit but if we want to sign a trade deal with the EU the extent to which we want to diverge will be crucial. And if we can persuade the EU to strike a FTA it will surely be the first in history where the two parties set out with the express objective of having their regulatory frameworks diverge over time. In that respect it will be the reverse of CETA.
Frankly, I would be amazed if the EU agree to this. Either they will reject it or there will be a Swiss style agreement where the entire treaty lapses if we try to vary things beyond what they think is reasonable. In other words the EU will have an effective veto over domestic law in this country. And it's hard to see the EU allowing us a reciprocal veto over the laws of the 27. We will be a rule taker and be in the humiliating position of having to run our draft laws past the Commission. I can't see the Conservatives accepting this.
We are still into having cake and eating it. The whole idea of free trade agreements is to have regulatory convergence to avoid one side gaining an unfair advantage.
It doesn't take a genius to see the "deep and special partnership" Mrs May wants to negotiate will founder because we don't actually want it that deep or that special. This is our usual problem, Britain thinks rules are for other people.