At the high school where I work we have had a pigeon problem for years, not helped by the fact that kids drop food scraps etc, so there is always food for the flying rats. A few months ago poison baits were laid and have been successful, as we haven't seen pigeons since then. Sparrows have come back, and they haven't been seen for a long time.
The joke is....they have moved down the road to the primary school instead!