Most local authorities will start by trying a package of care on a daily basis to keep the person living safely in their own home.
This initial period may be free, during the assessment period (usually about 6 weeks)
This POC is then means tested,and usually if she has more than around £24000 in savings, excluding the value of her home, she will have to pay for her care. Costs vary around the country but average between £10 to £18 an hour
Things like a meals on wheels and encouragement to use day centres etc may also be suggested.
In addition small pieces of equipment may be supplied , such as grab rails and raised toilet seats, to minimise risks of falls at home.
If your Gran continues to struggle at home a residential home or nursing home may be the next step.
If she owns her own home, and lives in it alone, she will be self funding her place, i.e. either sell the property or raise an income from it through rental.
She will cease to be a 'self funder' when her capital approaches around £24000, but again this figure varies around the country.
And then the local authority should take over paying the fee.However if the LA is paying the fee her chosen home may not be one with which it has a contract and she may either have to move or the family may have to pay the difference between the LA contribution and the actual home's fee.(It's called topping up)
She can expect to pay anything between £400 to £1200 a week, agian depending on the area she lives.
As you probably know both political parties have made care for the elderly a big issue, so things will probably change over the next few years,
You should also look at www.cqc.org.uk which inspects all care providers in the UK, including care agencies and homes.
Finally, but most important of all is what does your Gran want to do?
Unless there is very clear evidence to the contrary it will be assumed that she has the mental capacity to make her own decisions, despite what ever others,no matter how well intentioned, think is best for her.
hope this helps