I can't speak for pigeons, as we don't have many here, but I successfully kept most of the caterpillar attack at bay last year by planting my vegetables in a polyculture. I basically sowed the seeds by broadcasting them over the beds, taking care to mix up six or more different kinds of plants together, vegetables and flowers, and many different heights. I also let weeds come up where they wished (though I chopped and dropped if they grew too big), and the result was such a huge mess of vegetation that the cabbage white butterflies didn't stand a chance. I watched them fluttering around the garden looking for the cabbages they obviously knew were there, but could not find.
I have also witnessed wasps catching and dismembering those white butterflies in my garden (apparently they take them home for the kids to munch, as the adults only eat nectar), so I try to maintain an insect-friendly habitat with plenty of flowers and weeds.