To be honest, £2816 a month doesn't sound excessive, if you factor in the rent component, utility bills, food and staff costs, but it seems many people are paying more than this.
To answer the previous question, I pay per month (approx):
£825 rent
£135 council tax
£120 food (without preparation)
£200 bills (water, gas, electricity, TV/phone)
So if I lived in a residential home, I'd be saving £1280 a month. That would leave me with £1616 a month to spend on carers and admin. The cost of employing somebody with on costs (NICs, sick/holiday pay, insurance etc) is probably double the amount paid to the workers themselves, so (say) £16 an hour, which would buy me about 100 hours of care (ie three hours a day).
That's before any profit which a private provider could reasonably be expected to make.
(I'm thinking aloud. It doesn't really help with the issue of who pays.)