Hi Bodhi, welcome to TP
It's difficult to answer the question because there are many types of care home and the rates vary. You say this lady needs feeding so her condition must be advanced, I would guess that this means that she also needs help with personal care, possibly is incontinent. That could mean a nursing home or an EMI (Elderly Mentally Impaired) nursing home either of which cost more than a standard care home.
The quality of the homes vary from the 5 star hotel look to the more basic and anyone looking for a home will have their own expectations about the standards they want.
You say they're paying a "ridiculous" amount of money, in a a very nice environment someone who needs EMI nursing, in south London...anything over about £2.5k a week sound ridiculous to me and anything under £1k pw probably doesn't exist.
You would get a lot more for the money if you moved them outside London. it may be inconvenient for the visitors but if it gets her better care then it might be worth thinking about.
If anywhere is suggested you can look up the report on the Care Quality Commissions website, they are the official body that inspect homes to ensure they are meeting the required standards and report on their findings.
K