The councils were responding to a letter from Stewart Murray, the GLA's assistant director of planning, to Bedford Borough Council in March during a consultation on the draft Further Alterations to the London Plan (FALP).
The FALP sets the capital's ten-year housing target at 42,000 homes a year, but outlines an annual housing need of between 49,000 and 62,000.
In the letter, Murray said he wishes to "strongly advise" the council to take account of a potential gap between housing supply and a growing demand in their local plans.
The councils' letter to Murray warns of "widespread concerns that (the FALP) potentially undershoots the provision of future homes that London needs".
They say Murray's letter "could be interpreted as suggesting that local authorities beyond London may need to play a part in making good any shortfall in supply".
The councils express "real concerns" about this, stating that South East authorities "cannot possibly come to a realistic view on what level of need London might be failing to plan for or provide and what proportion of that failure it should seek to plan for in its development plan".
Any need for the South East to contribute should be "tackled in a strategic and collaborative way" within the context of a "fundamental review" of the London Plan, it adds.
The authorities ask Murray for "confirmation that there is no intention or expectation for local authorities outside London to specifically plan for any level of London unmet need".
Catriona Riddell, the Planning Officers Society's strategic planning convener, said: "The surrounding authorities are in an impossible situation.
"The Mayor’s ‘softly, softly’ approach means that they have no idea what’s expected of them in supporting London’s growth."
Sir Edward Lister, the GLA's deputy mayor for planning, said the Mayor was "not asking councils outside London to take London’s unmet housing need" but was "simply recommending common sense, coordinated regional planning to ensure London and the south east’s housing needs are met over the coming years".