Hi
I'm 3 years into this. Mum about to go into a home. Dad now has a live in carer (cheaper than a cleaner coming in, more flexible for him and more consistent staff). I feel for you.
Some GPs have a social prescriber who aims to bridge the gap between a GP and clients. Ours has been a god send. She has chased up the pathway, helped with carer lists and generally been a rock. She also helped my Dad come to the realisation that he needed carers, which he might not have taken from me.
Also Dementia UK have a service where you can book a 45 mins chat with a trained person. I found that very useful. It helped me get over the shock.
It's Alzheimer's UK or Dementia UK that have a forum where you can search for info.
With carers, try and get recommendations. Be really clear about what you want. We went through 3 agencies before we found the right one. They weren't awful just not right for them.
Age UK have activities in our area to take people but less active involvement.
I had to fill in a form for the Attendance Allowance. It's not means tested and as you have a diagnosis - it'll be backdated to that point. You can use it for whatever you want, the money is just paid into the account. It might help pay for a little extra help. Also, apply for a reduction in council tax, since your mum's diagnosis means that this is offered.
Make sure that a Lasting power of attorney is done for both mum and dad. The forms (health and welfare and finamce) is on the govt website. It's not difficult to fill in, getting the signatures in the right order is a bit tricky. You don't need a solicitor. I kept mine and my parents as brief as possible as you don't want them to specify too much (e.g.id like to go dancing every week), as your tastes/abilities change. It's better to do a later sheet which just guidance which you file with it.
Everyone's dementia journey is different. Alzheimer's UK have a set of stages they say people go through, my mum has had a bit of one and a bit of another.
It'll be worth getting some paid help for your Dad. You might want to paint it as a housekeeper or cleaner rather than a carer.