So sorry for your loss NainCC, it doesn't help that so much has to be done when you are feeling so numb.
My husband died unexpectedly in 2016. My kids were 20 and 22 and unable to come to the house because of their grief in the early days, so I was alone with it all.
I was in such a state I got our solicitor to handle probate for me.
I did all of the other admin, and kept notes on a lined pad, and had a notebook with notes of the action I'd taken. I paid for 10 Death Certificates, and kept a file of all correspondence in chronological order.
The worse thing for me was 02 - they wouldn't speak to me, and my husband paid the contracts for all of our phones. At the time the bank wasn't allowing me access to his account, as I was waiting for probate. I was told I'd have to go into the shop twenty miles away with his death certificate, and at the time, I was having panic attacks driving. I screwed up my courage and did go, about week 3, and showed the young man the death certificate. In a very off hand manner he said 'we don't need that'. I was so upset, and complained to their HO, it was such unnecessary stress.
The most important thing is to get your house into your sole name on Land Registry, if you are doing your own probate, action that as a priority.
Do remember to be kind to yourself, until someone walks in our shoes they have no idea how hard it all is, do accept all offers of help.