Heston House, in Old Vicarage Farm, Heston, will shut over the coming months, with the council promising to find alternative accommodation for the 31 people currently living there.
Leaders at Hounslow Council, who approved the closure at a cabinet meeting on Tuesday (June 16), said the accommodation was no longer needed as more elderly people are choosing to live in their own homes.
Councillor Kamaljit Kaur, cabinet member for adult social care and health, also said the building was not up to scratch as residents do not have private bathrooms, which she described as a basic right.
She said it was a "difficult decision" to make and promised to ensure everyone's needs were met when they were transferred, meeting residents and their families herself if necessary.
Cabinet members voted unanimously in favour of the closure, despite an impassioned plea from Najam Hassan, whose 89-year-old grandmother Naseem Sheikh lives at the home.
He accused the council of taking a "short-sighted" view, given the borough's growing elderly population, and raised fears the upheaval of moving could affect residents' well-being.
He also pointed out that the council's two remaining residential care homes for older people, Sandbanks in Feltham and Clifton Gardens in Chiswick, were respectively rated 'requires improvement' and 'inadequate' by the Care Quality Commission - the same watchdog which had recently given Heston House a clean bill of health.
"Is it in the residents' best interests to move them into homes which are substandard according to inspectors?" he asked.
An online petition, started by Mr Hassan to save Heston House, has been signed by 623 people, and many of the users, their friends and relatives were in the audience at Tuesday's meeting, where they held aloft posters urging councillors to save the home.
Ms Kaur claimed action plans to improve care at Sandbanks and Clifton Gardens were already being implemented and she would not move residents anywhere which was not providing a good standard of care.
Although Mr Hassan claimed those two homes had only seven vacancies between them, Ms Kaur said she was confident there was sufficient space in Hounslow and surrounding boroughs to accommodate Heston House residents, be that in council, voluntary-run or private housing.
Ms Kaur said Heston House would not close overnight as each resident would receive a personal assessment before being given options about where to move.
Day care services currently available at Heston House, meanwhile, will continue to be provided at Sandbanks or Clifton House.
Although the closure will save the cash-strapped council an estimated £758,000 a year from 2016/17, as well as eliminating the need for a £5m refurbishment, Ms Kaur insisted the decision was not financially motivated.
She said the council was concentrating on supporting older people to remain in their homes or at extra care housing, where residents have their own front doors but access to communal areas and support, as this was what most people wanted.
One member of the audience said most people at Heston House could not use the bath by themselves due to their disabilities, so it was wrong to use the lack of private bathrooms as an "excuse" to close Heston House.
But Councillor Richard Foote said his father had lived at Heston House for two years and, although the care had been excellent, he had "really wanted" his own bathroom, which was not available.