There is a poverty that, rightly, the Church teaches should be eradicated. This is that un-chosen poverty that leaves the human person without dignity - without sufficient means to meet their daily needs of food, health, accomodation and participation in society. I expect that in some places poverty of this type is part of the story of the riots.
But there is also a second poverty, a chosen poverty, that the Church encourages as part of the way in which Christians respond to the challenge of living the Christian life. In its strongest manifestation this is seen in the vow of poverty typical of the life of religious orders.
Can. 573 §1. The life consecrated through the profession of the evangelical counsels is a stable form of living by which the faithful, following Christ more closely under the action of the Holy Spirit, are totally dedicated to God who is loved most of all, so that, having been dedicated by a new and special title to His honor, to the building up of the Church, and to the salvation of the world, they strive for the perfection of charity in the service of the kingdom of God and, having been made an outstanding sign in the Church, foretell the heavenly glory....
The Church encourages her members to promote the value of this chosen poverty, freely entered in to, in the life of the Church. If religious life is understood as the most radical form of living that life that should be proper to all the Christian faithful - a thought, I think, that can be found in the writing of Louis Bouyer on monastic life - then chosen poverty becomes something in which all the faithful have a stake. Different vocational contexts mean that this counsel of poverty will be lived analagously, or "according to state of life". The fruit of this is a certain detachment from material goods, a recognition that some material goods are "surplus" and not necessary, and can be dispensed with.
Within the dynamic of theft that was part of the recent rioting in English cities, an excessive desire for possession of "status" consumer goods played a part. Clearly those who gave in to temptation, or who engineered the looting of these goods, bear a prime responsibility for their actions. But we should also recognise that many others have shared in creating a culture in society that values the possession of status consumer goods in a quite inordinate way.
A contribution that the Church can make to the debate about the riots is:
(1) to offer the example of voluntary poverty as lived by religious in our own cities, to talk about this in the media and to encourage its visibility in the life of parishes and dioceses
(2) to promote in parishes and schools the idea of a certain "detachment" from material goods
(3) to encourage the presence of religious in the deprived areas of our cities, and to encourage social action on the part of Catholics in those areas
(4) not to be shy of offering these examples, explicitly religious in their inspiration, as contributions to a common good for which others in society also work.