I have lost weight but have been combining running with careful changes to my diet and I'd estimate that the running only contributes about 20%, perhaps more now that I'm running much longer distances. It has made weight loss through dieting easier rather than causing weight loss in itself, I think. My body shape is roughly the same but my legs and bum are much more toned and in general I feel strong and fit, which is a really good feeling.
I think a lot of people start running assuming the pounds will just fall off them (because it's hard at first and you kind of imagine effort = weight loss) but unless you're running a fairly significant distance you're not burning that many calories. A rule of thumb is 100 per mile. So if you run 5K, that burns around 300 calories, which is not bad as long as you don't come home hungry from your exercise and immediately raid the biscuit tin or whatever.
And of course while you're working up to the 5k you're burning quite a lot less - the C25K programme probably burns around 150-300 each time you go out and it takes a deficit of 3,500 calories to lose a single pound of weight. So it's not a miracle weight loss method in itself.
However, I don't mean to be too negative as (1) the general health benefits of running are amazing, (2) you will increase your metabolism and so will burn calories much faster, (3) if you're careful not to eat back the calories you do expend, then of course you will lose weight faster than if you don't exercise at all and (4) you will build muscle which is so much better than flab.
PS Am not remotely an expert here; these are just my own observations and I'm sure more knowledgeable people can add further running benefits to my list.