It is also expected to coincide with a Labour Party paper to examine, among other things, proposals that councils take over purchasing responsibilities from district health authorities.
Both Wandsworth and Sutton are objecting to a series of local developments, such as the proposed merger of Sutton and Merton District Health Authority with Wandsworth DHA and the threatened closure of local hospitals.
A report by Sutton's assistant chief executive Mick Lowe laments the fact that the residents of Sutton stand to lose from government reforms separating purchasers from providers and introducing an internal market to the NHS.
'The introduction of the internal market appears to be establishing a regime that is answerable only to the provider market and not to patients, residents or potential health service users'.
Mr Lowe says the changes would create 'a far larger and more remote health service purchaser and a far larger and more remote health service provider, both with no local accountability'.
Wandsworth is also expected to appoint consultants next week to examine further the benefits of giving the DHA's purchasing responsibilities to the council and to draw up a proposed timetable for the transfer.
The consultants will also be asked to investigate the new NHS capitation funding mechanism which is expected to cost Wandsworth up to £24 million. The council's proposals have been rejected by the Department of Health.
Both Sutton and Wandsworth have stressed council health care purchasing would restore local accountability to the NHS. It would also bring together health responsibilities with wider factors influencing general health such as environmental services, housing, social and leisure services.