The national grid runs at 50Hz
Most of the time. However, measuring the frequency is precisely the means of activating the power station in a mountain at Dinorwig when it is needed to provide backup in a hurry. Generally four turbines are kept synchronised with the grid and a reduction in grid frequency automatically opens the water valves for them to start generating. There are other ways of starting them up too, but measuring grid frequency means this can be done in an emergency long before humans would have reacted.
and is guaranteed to vary by less that a gnats hair
The number of complete cycles in a day is still I believe the major standard. Only two things in life are guaranteed and neither of them are to do with the electricity system. The frequency in parts of England was zero when Sizewell B (a "highly reliable" nuclear plant) failed, followed very shortly afterwards by the working units at Longannet (I can't remember if it was one or two units of the installed four which were working, one was certainly being fitted with flue gas desulphurisation equipment and at least another one was off for another reason (perhaps maintenance)).
Generator frequency can only vary from grid frequency when it is disconnected from the grid.
Or if the generator is not directly connected to the system.