The council decided that it would be better to replace its network of centres with personal care options for those who currently attend the centres, aiming to provide a more modernised level of care with the aim of better integrating those needing help into their communities.
It will also help the council to save Â£3m, at a time when its budget is under severe financial pressure.
However, the decision has been hugely unpopular, with more than 70,000 people signing a petition against the changes, which was due to be presented to the council.
But legal action has also been launched against the authority's decision and although specific details of that remain unclear, the council's own rules state it cannot accept and discuss petitions in such circumstances.
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Protest group members still attended, however, with a bagpiper to help draw attention to their presence as councillors assembled for the meeting.
Organiser Robin Symonds said: 'My sister attends a centre threatened with closure. I think it is grossly unfair, what the council is proposing to do.
'I think it will have a devastating impact, there are literally scores of service users and carers who have no idea what they are going to do when the centres close.
'This is their lives; the council say they should integrate into society but that doesn't work for everyone.
'They will be sat at home with no stimulation and nothing to do. I don't think you can overestimate the impact it will have.'
The council wants those currently attending day care centres to have personal carers instead, financed through personal budgets.
However, relatives and carers have questioned whether it will be feasible to find enough people who can provide suitable levels of care to meet the needs of those currently attending day care centres, which are credited with providing a positive experience for the users, as well as an opportunity for respite to assist relatives.