The ZF 8 speed box can lock up from just 1200rpm in the 2nd of it's 8 ratio's so torque converter losses are kept to a minimum. The 8 ratio's allow the engine to be kept in the most efficient rev range more of the time and the taller 8th gear allows for lower revs at higher speeds.
So yes it's easy to see why the ZF 8HP is much more economical than earlier conventional auto and can match or exceed manual and dual clutch boxes.
But as others have said at £1500 it's still going to be added cost even if you do a lot of miles and even if you get some of the costs back when you sell.
The reason to buy is because it's probably the best automatic box on sale today and it makes the 1 series a joy to drive. On top of that I felt the manual box was notchy, very stiff when cold and the gear lever had a springy feel (116i, 118d, 120d). And on RHD cars the pedals are very offset in the manual.