The minimum octane rating available in the UK is 95 RON (Research Octane Number). I understand the US uses a different octane standard - the Anti-Knock Index (AKI), and often written on pumps as (R+M)/2. It may also sometimes be called the Posted Octane Number (PON). The UK 95 RON fuel roughly equates to a US rating of 90. We also have super premium petrol with a rating of 98 RON. Many claim this give 10% better fuel economy but I didn't find much difference. My dealer did tell me you need several fuel tank refills for the car to 'learn' the fuel grade. There was no mention of needing to retune the car.
Yeah, within reason, the car can technically "tune" itself for better octane fuel. It takes a few tanks full, and only nets you about 2-5% more torque and [arguably] maybe a mpg or two. However, it is not a true tune, but, rather, that the anti knock sensor backs off of its parameters just a tiny bit because higher octane is less volatile.
the lower the octane fuel, the more the knock sensor slows the ignition of the gas/air mix in the particular triggered cylinder due to the potential to knock, or premature detonation of the air/fuel mix. This process saves the engine from damage/knocking at the expense of a tiny bit of power on 87.(But it is more significant with sub-87 octane and your car will run like garbage.)
In the end, if gas prices are like where I live, where 91 costs nearly $.50 more/gal than 87, then it likely is not worth it because the gained power is very minute and imperceptible. If 91 or 89 is cheap where you live, then I'd say go for it.
Hope this helps!