The Episcopal church I attended as a child did a large-scale procession for Palm Sunday and Corpus Christi. I went to a HCCAR parish off and on for a while and they did processions quite regularly. They had processions for Ember Days, Rogation Days, and a number of feasts throughout the year. Now as a Roman Catholic, I've been involved in a lot of processions. I've done a few with the Ordinariate of the Chair of St. Peter. Most have been through my Abbey. We do a large procession on the Feast of All Souls with family members of the living and deceased members of the monastic community as well as a large number of local families. We do processions for Rogation Days, Palm Sunday, Holy Thursday, Corpus Christi, Candlemas, the Feast of St. Benedict, the Feast of St. Scholastica, and the anniversary of the founding of our Abbey.
We have a procession during Palm Sunday, beginning outside and moving into the nave. Nothing wrong with processions per se... although we Anglicans don't want to be parading wafers around in monstrances, since rendering worship toward the image of bread in the monstrance would be contrary to the prohibitions found in Exodus 20 and Leviticus 26.
I would rather the liturgical procession than the processions we see presented in the politics of our various nations. I note with amusement that England goes to the polls on American Independence Day and America goes to the polls on the day of the running of the Melbourne Cup. The trifecta would be if Australia went to the polls on April Fools Day, but sadly that falls on a Tuesday and our polls are on a Saturday