Louisa Goldsmith broke her leg and collar bone in a fall on 25 May and has since been a patient at the Chelsea and Westminster Hospital - although doctors said she was fit for discharge after just two weeks.
But Wandsworth LBC insists she is now so frail she would be better off in a nursing home.
Mrs Goldsmith's daughter, Linda, is now mounting a judicial review challenge to the council's stance, claiming it violates her mother's human rights.
But, after anxious negotiations outside court, the council today agreed to convene a 'round table meeting' in a bid to resolve the impasse.
Wandsworth's barrister, Elizabeth Laing, said the council was 'anxious to co-operate' with Linda Goldsmith to thrash out the best way forward for her mother. She will be able to attend the meeting, together with medical professionals and local authority representatives.
And Jenni Richards, for Mrs Goldsmith, told Mr Justice Burton: 'It may be the discussions resolve the matter, one way or the other, finally.'
But the judge set a strict timetable for the case to return to court as a matter of urgency on 13 or 14 October 13, unless agreement is in the meantime reached over Mrs Goldsmith's future accommodation.
In her written submissions, Miss Richards told the judge: 'Mrs Goldsmith does not need to be in hospital and asks every day to go home.'
When she moved into Mary Court in 1996, she had been promised 'a home for life' and she had a 'legitimate expectation' she could stay there.
Mary Court is 'a familiar environment which she regards as her home' and the council, argued Miss Richards, had failed to consider the risks of moving her to the 'wholly unfamiliar environment' of a nursing home.
She said the council had not involved Linda Goldsmith in decisions crucial to her mother's future care, had given no adequate reasons for its decision and had failed to deal with the dispute in a 'transparent' manner.
And the barrister argued the council's stance violates Mrs Goldsmith's right to respect for her home and family life enshrined in Article 8 of the European Convention on Human Rights.
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