I've read a lot about this issue. The Elise is a neutral car which car corner at high speed, but it lacks power oversteer, so if you push the throttle when exiting a bend and you expect the tail to come to the front, it wont. The car will understeer. That's a little disapointing, since it's one part of the fun of rear-wheel drive cars. I don't know if this is a common issue to all mid-engine cars or has to do with the narrow front tyres of the Elise. However, it's surprising that Top Gear claims that this doesn't happen to the VX220, which is basically the same car with the same tires.
Another video in which you can see this lack of power oversteer is the one with the SC review by Jason Plato. He complains about the impossibility to take advantage of the extra power as he presses the pedal to the metal in the middle of a bend and he says all the car does is wheel spinning (go to 2 min 30 secs):
On the other hand, the Elise has a tendency to show lif-off oversteer, which can be dangerous if you're not used to it. If you change down gear in the middle of a bend or lift the throttle suddenly while in high revs, the car can have a sudden oversteer, and I've heard it's very difficult not to end up with a spin. So, it's good to remember to use the steering wheel and the throtle smoothly through the bends, and use the heel-toe technique if you have to do agressive downshifts with this car.
As regard the Top Gear video, as you have already said, Gavin uses speed and weight balance to drift the car. You can even see a little of the scandinavian flick technique. That way you can have oversteer even with a front engine car.
There's another video by Top Gear in which they insist in the VX220 superior handling, with a comparison of both cars taking the same bend (go to 1 min 05 secs). I may be wrong, but it seems that Clarkson has a clear sympathy for the Vauxhall over the Lotus and tends to overate it in all aspects.