There are numerous galleries and visual arts organisations in London that work outside the gallery in the public realm, often through partnerships with other organisations such as housing associations or local authorities. Most also have education programmes working closely with local communities, including young people.
A local visual arts organisation is often invited to join a steering group. They often know the area well and have sustained links and may also understand the kinds of projects that have been successful.
It may be possible to work in partnership with a gallery to commission new work, but this will always depend on the direction of the gallery's own programme, as well as the funding that is available.