Yes, combined, yes diesel. If you want to sell a hybrid here it has to be more efficient than a diesel. This car will not be 30-50% more efficienct than the diesel.
The Prius is rated 65 mpg in the UK, for comparison to the 67 mpg of the 1.4D Yaris noted above. I agree that the Prius C is not going to best the Prius by 50% in fuel economy, but it is already competitive with supermini diesels at no better than current Prius fuel economy. This is a very nice place for Toyota to be in Europe so long as the purchase price is competitive.
With Prius v using the same 1.8L engine, I would think Prius c will share the same part to keep the cost down. I wish it has a smaller engine but 1.8L is an amazing engine especially with the EGR (eliminates pumping loss at low load).
My guess is that the Prius C is Toyota's first foray into the 'well under $USD 20k' market segment with HSD. I have been waiting a long time for this to happen, and I think it is GREAT. And as I mentioned above, this car will hopefully give them a nice alternative to supermini diesels in Europe, which is a segment they have not really stood out in thus far.