First you need to decide whether you want to do this - if you're currently not working, have the time and could do with the money, it could work well. You'd be about £10k pa ahead of all the women who do this sort of thing for free, for a start.
However, if/when his needs change, will you want to continue. Do you and he get on? You mention helping him with meals and bills. Is what they want achievable in the time stated? Does he live close by? Are they asking to you wash and dress him and would you do this? Are you capable of doing the job? A professional carer could be more appropriate.
But this could be seen as one of two situations - the role is either similar to being a self employed cleaner or they're employing you as a carer - so you need to decide on this before working out how to declare the income. If you're self employed, which I don't think you are in this situation, you would need to register as such and submit a tax return, although you'd not pay tax if this was your only income.
However if they're employing you, they need to comply with employer's requirements, as they would if they paid for direct care rather than engaging the services of a care agency. This could include paying employer's NI, and also paid annual leave, although I suppose it's up to you to decide if you would enforce this. I'm sure there's advice online about responsibilities for employing someone to work in your home.
Either way, if you claim UC, you'd need to declare it as income.