What about the poorer, more crime-harried communities? Who is campaigning there for a better social fabric? As it happens, quite a lot of people and quite a lot of organisations are - ranging from self-help groups to educational and campaigning organisations such as the Phoenix Centre in Birmingham.
One of the most interesting recent developments is the growth of "people power" organisations based on churches, mosques, synagogues and Hindu temples throughout England.
In their statement of aims and ideals, the members of the Citizen Organising Foundation quote Proverbs 29 v.18: "Where there is no vision the people perish."
Mrs Lawrence would doubtless agree. But what do they mean in practice? Yesterday, The East London Communities Organisation (Telco), the sixth member of the foundation, gathered to hammer out strategy for their first meeting with Sylvie Pearce, chief executive of the London Borough of Tower Hamlets.
Telco, an example of a new flowering of community organisations in inner- city Britain, is to be officially launched at a meeting on 20 November attended by MPs, business and religious leaders and up to 1,300 supporters with "an agenda for justice about jobs, low wages, discrimination, poverty, schools".
But if that makes it sound like any number of other socially concerned campaigning organisations, the major backing from local religious centres alongside tenants' associations and community groups brings with it a strong sense of moral mission.
Neil Jameson, the foundation's secretary, said yesterday: "Mrs Lawrence doesn't have a tool to achieve what she wants to achieve and that's really important. We believe we have the techniques."
The morality is nothing abstract. Instead, it is a strongly grass-roots effort to make the world a better place.
Mary Moylan, of St Catherine's Roman Catholic Church, Bow, and the Filipino Chaplaincy, said: "It's moral in the sense of bringing the values of humanity. When you mention the word morality, it sounds like sitting in judgement. This is nothing to do with judgement."
Jason Wu, a Buddhist working with the community in Shoreditch and Hoxton, said: "If it's morality, it's morality that's organised and broad-based. It's about relationships - relationships with the power-players."
But for Joy Coogan, of Alpha Grove Community Centre, Isle of Dogs, said the point was standards, not morality. "The community wants to improve their way of life. Morality doesn't come into it."
Paul Bunyan, a youth worker with the Citizen Organising Foundation, said meeting Ms Pearce of Tower Hamlets council was an important step towards achieving their aim of giving the people of east London a way of acting on their values and ideals. "She is a very significant person. If we're going to effect change we've got to get into a relationship with her."
The approach is a mix of working-class idealism and religious humanitarianism. If Frances Lawrence wants a practical model for bringing people together perhaps part of the answer can be found in the rawer and grittier world of Telco.
R David Muir of Mile End New Testament Church, the largest Pentecostal church in the country, expressed it quite simply. "It is people working together for the common good," he said.