In their first appearance in "Blink", it was indeed their final undoing. After the TARDIS dematerialised, the four Angels, which had each been holding on to a corner, were caught staring at each other, which made them turn to stone.
If you mean how they could move in "Flesh and Stone"... It may be because they were more powerful due to the radiation. That and they weren't actually looking at each other, not in the eye at least. They can probably look at each other or in that general area.
Another more plausible explanation is that there were thousands of other angels, all trying to turn out the lights. That would have provided moments of darkness long enough to disengage their defense. In "Blink"," if the light bulb burned out, or there had been another angel to turn it out, the four would have been released. However, it is unlikely that there was another Angel, and the four scavengers would have started to deteriorate by the time the bulb burned out.