Gracesgran Pension Credit is not automatic, you need to apply for it. From the sound of it your mother should be receiving Attendance Allowance, the disability benefit for those who become disabled after state retirement age.
Carers allowance does not go to the disabled person, it goes to the person looking after them for at least 16 hours (I think) a week. If that person is also over retirement age that generates no cash but does increase the upper limit on Pension Credit. If the person doing the caring is working, as vampirequeen says the money is cut off as soon as their earnings reach £100 a week.
To think that London, or anywhere else for that matter, does not belong to any one demographic