No. Steak needs be seared at a high, high temperature. Not only would extra virgin olive oil lose everything that makes it special at such a high temperature (so not worth the expense anyway), it would also burn. The smoke point of EVOO is 350F, 180C (give or take). That's simply way too low for searing steak.
There is no such thing as a cooking oil that's hot enough to heat to what I would consider ideal steak steak searing temperature.
(I just used this picture in another answer, that's Celsius by the way)
No cooking oil can withstand that kind of heat. So how can you get away with it? Well, when I do it, first I remove the batteries from every smoke detector in my apartment and open my kitchen windows. Secondly, I choose a very refined (read that tasteless) oil with a high smoke point. By using a refined, tasteless oil, there's really nothing left after it burns to taste nasty; it just tastes like char, something I want anyway. Third, I don't put oil in the pan, I just lightly oil the steak. The method works great, but it requires a cast-iron pan and a high smoke point, neutral oil.
I'm not crazy about Jamie Oliver's method because I like a serious char. You can tell he's not using extreme heat, because he's using a non-stick pan. I assume he doesn't throw away the pan with every steak. Even with his method, EVOO would be a bad choice of oil. The point at which extra virgin olive oil gets nasty is significantly lower than the temperature that will ruin a non-stick pan 400F+ (200C+), and much lower than the temperature necessary to get a decent char on a steak. Refined (pure, or extra light) olive oil would be an OK choice, as would canola, safflower, refined avocado, grapeseed or soybean.