As Indeedido posts an assessment of your relative needs is required by a relevant professional. The social services department of the local council have the details. The medical assessment is free. After that a financial assessment needs is likely to be made. Based on both of these a decision is made by the NHS and social services of who is responsible for the fees. Then the relative and the family have to decide how to pay, if they are responsible. The family and the relative should select the home, but Social Services of the Council and possiblly NHS can help. Not all homes are the same. A Nursing home has a nurse and can cope with higher needs. A Care home will usually bring in nursing support when needed from a GP practice. Nursing homes are more expensive. Homes nowadays often have parts/floors for people with dementia and non-dementia. The Care Commission inspect homes and publish reports online like Ofsted. Read up on interested homes. They are only guides, but often useful.
Someone mentioned DOLLS - they may mean Dols (deprivation of liberties) - Its a legal document and procedure that has to be completed when a elderly person hasn't or can't agree to go into home. Medical staff, Social Services and Care home staff work together to complete this. Family and the person concerned have to be fully consulted. The person affected may have an advocate somebody to speak on their behalf.
TC - you may have a lot to learn. I was the same I know nothing say in March 2020. If people have followed some of my posts they know I and some of my relatives and my dear parent have been on a h*ll of voyage in just 2 years. Hopefully you will not have to deal with Covid. (3 Care Homes, 2 Rehab centres, 4 significant hospital admissions, home help organisations, social services managers, social workers, different hospital departments, Care Commission etc).
TC - reading your post if the person concerned has a very good income or their family do they can skip the financial assessment and just say they will pay say £900 to £1100 per week privately, without any support. Most people don't and thus have to sell their property when they go into a home.