Wow, things are different on my side of the pond. When we got married, my love and I gave out the gifts at home before we left for the church. We were all congregated at my parents' house for pre-ceremony photos. That way, the bridesmaids, ushers, etc., didn't have to worry about where to stow them during the festivities.
When we distributed everyone's boutinierres (spelling?) and bouquets, we had the flowers on a table with champagne and the presents beside them. As everyone claimed their flowers, we toasted them all and presented the gifts. It didn't take long (maybe 15 minutes), and it gave us a few private moments with our "special people" before the madness began in earnest.