I'm in Wales and I don't know how much things vary around the UK but this is my experience.
Mum lived in a granny annex in our garden. She had very limited mobility - had to use a zimmer frame or wheelchair to get from the bedroom/bathroom to the sitting room, unable to dress/undress, prepare meals/drinks.
After much back and forth between me and the surgery mum eventually had a visit from a social worker at the beginning of November 2019. We heard nothing from them again even though I chased it up every couple of weeks until the beginning of March 2020 when a young girl turned up on the doorstep as I was getting mum up and introduced herself as coming from the care agency! Mum had been assessed as needing two calls a day - morning and evening - and I was already providing the rest of her care.
Someone came for 45 mins in the morning to help her dress, get her into her armchair and give her breakfast. A different carer came in the evening to help her to bed. The times were variable! Mum had said she would rather get up late and go to bed late and it was often 11 o'clock before the carer came to get her up and they came around 9 o'clock in the evening. Once mum was settled in her arm chair with her breakfast the carers would potter round and do whatever they saw needed doing in the time they had left - make the bed, wipe over the kitchen, put the vacuum round. The kitchen was pretty much unused - I would cook in my own kitchen and bring her meals to her and put the crockery and cutlery into the dishwasher so it wasn't like it needed a major clean. My daughter would clean for her every week as well so there was no need for regular housework from the carers.
We had to complete a financial assessment and mum had to pay £100 a week. She would ask every day who would be coming for the rest of the week and we would fill it in on her calendar as she was uncomfortable with a stranger walking in. We had a key safe by the door and the number was shared with the care company.
I really appreciated the carers coming - it meant that I didn't have to go in and out to mum in the morning - it had got to the stage where I could go in to see her and if she was ready I would do her breakfast in bed, go home and go back when she called me to say she was ready to get up. It meant I didn't have to stay with her until she was ready to go to bed - she liked to stay up until 11 pm and then would want me to help her into bed so it was often 11.30/11.45 before I could leave her.
I wasn't aware/was in denial that mum was in the early stages of dementia (a whole other story) and she was very unreasonable about the need for carers. She wanted me to pay them because they were coming to help me, not her. They were coming because I was too lazy to give her a little bit of help. Mum liked the majority of the carers, a couple she wasn't keen on, for no good reason. But again I think that was to do with the dementia.
For me, as her carer, they were a lifeline and enabled me to have a couple of hours in my own home that I wouldn't have had without them.
As the dementia progressed I realised aware that we needed more help and I was getting to the point where I was going to ask for her to be assessed again then she had a fall, ended up in hospital and went from there to a home.
I really appreciated the carers, as your dad might, and mum tolerated them because I refused to back down.