They say that taxi drivers and hairdressers know everything, so on the basis of a conversation with a Corporate Cabs driver taking me to the airport, and bolstered by some 20c/litre supermarket discounts, I've been fuelling the Jeep's V6 with premium. The taxi driver, who claimed to keep detailed records, said his Caprice got much improved mileage using premium and that the savings more than paid for its extra cost. I've had a couple of tanks-worth through my thirsty 3.8 litre and, doing the same mix of driving I did on 91 octane, seem to be getting around one litre per 100km better. I'll stay with it for a few more tanks-full and work out the overall improvement and whether it has been cost-effective. And no, I haven't noticed any improvements in power or smoothness.
Comments invited from readers who have been down the same path, with any make or model.
UPDATE: My test was flawed as it wasn't possible to replicate the driving I did using 91 octane. But after doing similar driving on several tanks of BP 98 I'm thinking there has been a small improvement, but certainly less than one litre per 100km and not worth the extra cost. That doesn't mean that your engine won't provide better economy on premium. I noticed no improvement in performance or smoothness, although others report quite differently (see comments, below).