Mr Justice Charles, dismissing Greenwich's judicial review challenge, rejected suggestions that the elderly woman - named as 'Mrs D' - had been consciously 'dumped' on Greenwich by its neighbouring borough, Bexley LBC.
The judge said this suggestion implied a 'conscious act of bad faith', but added that Greenwich's lawyers had never pressed home the claim.
He expressed great sympathy with Mrs D and her family over a period of prolonged lack of contact from Bexley between May and June 2002 as she moved into her new Greenwich placement and while her position was in a state of 'flux'.
He said that 'nobody had informed Greenwich what was happening', which meant Greenwich did not have access to Mrs D's welfare review.
But he concluded: 'It seems to me that the lack of contact with Greenwich, and the discontinuance of contact with Mrs D and her family, occurred through an oversight'.
Greenwich took legal action after it was ordered by the Department of Health to foot the£150,000 bill for covering the woman's annual care.
Its lawyers argued that the health secretary's March 2005 ruling was legally flawed, and that Bexley should be responsible for her care.
Bexley was said to be liable for the care costs on the grounds that Mrs D - a lifelong Bexley resident - was 'ordinarily resident' in that borough, where she had owned her own home.
Originally placed in a home in Bexley she was later moved to the Greenwich care home in 2002 as she 'urgently required placement elsewhere', the judge was told.
The issue for the judge to resolve was whether the health secretary was right to conclude that Mrs D was not 'ordinarily resident' in Bexley. The decision was based on the fact that she had sold her Bexley home, and therefore severed her links with the borough.
He said 'some criticisms' could be levelled at the health secretary's approach, but added that 'at heart he has identified the correct criteria'.
STRAND NEWS SERVICE