Even if it's a private arrangement, and whatever the law, an experienced carer would and should keep a daily record, if only for his/her own self-interest.
It's a log of what you've done that day for the client and a record of their daily activities, for example when did the client last open their bowels, is the client walking well today, what did they eat, etc. Also very importantly, how is the client's skin, particularly pressure areas and peri-anal area.
If a whopping big pressure/moisture ulcer is suddenly observed by a relative or district nurse, who is to say how long it's been there if a record of skin condition is not kept?
The above is from a carer's point of view.
From a relative's point of view, don't you want to be able to ask how has my mother's appetite been, has she had visitors, did the district nurses turn up, did the GP visit?, etc?
If a daily record is not kept how is a carer to remember each and every detail of the past weeks?