Social Services apply their own assessment and threshold for services. It helps if the GP and other health professionals involved with your mother’s care writes to social services referring her for help giving details of the care help she needs with having her illness. A means test is also applied, based on income and savings. Anyone can buy care services privately.
It is the same when your mother moves in with you when you yourself are unable to provide the level of care she needs, you would be asked to state what help you can provide. But often people who look after a parent like this find they might be given little help until a crisis occurs, the constraints on budgets now has pushed things in this direction. Also it helps if your mother herself can indicate the tasks of daily living she cannot manage without help.
Being a carer is a demanding job and many find getting help from social services very difficult in the situation you describe. The new Care Act legislation allows carers to seek an assessment to be offered help in their own right. You will need to persist and if necessary challenge decisions if your mother’s needs substantial care.