Not tried anything Jamie Oliver (and I recongise that what I am about to say isn't really in the 'spirit' of the thread) but I can cook a suprising number of things in 15 minutes.
That said, to make some of the stuff I have to be organised and do all my chopping and prep work ahead of time when I have a bit of free time. Stuff like chopped carrots, celery, peppers, onions, lettuce, greens, prepped brussels sprouts, cababge, leeks, etc will all last a few days in the fridge and make life super easy. Frozen and tinned veg, beans, etc are also really handy. Sometimes a packet of pre-cut stir fry veg or soup veg or salad greens can also make life easy. More expensive, but if you get home at 18:15 and need to leave by 18:45 to get to band practice and you're starving, its worth it. Pasta cooks in 8-12 minutes, rice and egg noodles take even less time, basmati rice cooks in 10-12 minutes, eggs cook really quickly, small-fresh potatoes will boil in 15 minutes or so, or you can pre-boil potatoes and reheat-pan fry....
Rachel Ray always advocated pre-prep work on her '30 minute meals' -and I can vouch that it can make a massive difference.
I am sure I wouldn't be able to do a Jamie 15 minute meal without prep work - I would most likely chop my finger off instead....