Unless they are in an emergency and are busy with aviating, they will coordinate with their dispatcher on diverting, even if only to verify that the weather at the intended alternate is still favorable. Per the FAA regulations, the PIC and the dispatcher have joint operational control over the flight. Of course, at the end of the day, only the pilots have their hands on the controls, so they can make the plane do what they want—but from a legal standpoint, the dispatcher and pilot-in-command have equal & shared responsibility for the safe operation of the flight.
I realize this is a UK carrier and was operating in the EU/UK, but for the most part, the rest of the world uses the US legal framework for aviation as a boilerplate for their own civil code. Yes, there are some differences, but these are usually minor and more of "differences in quantity" rather than "differences in kind". [Since the airplane was invented here the US had a head start on regulating civil aviation.]