Hi Dominic,
My s type is a 2.7 diesel and I always us shell V power -- premium. It seems to suit the diesel engine, especially on a long run where my average performance is circa 46 mpg with a record 50.2 mpg on the M1 when there was a 50 mph speed limit for 45 miles. But a diesel is much different from the petrol engine.
37 mpg for the 3.0 litre engine does sound very good and keeping the fuel system cleaned can save a big bill. I would be inclined to use the premium fuel for a a while a see if you can feel the difference.
Regards,
Peter.