Hi op, sorry you're going through this. My mum died unexpectedly last year, and it felt overwhelming so I understand where you're at right now.
It sounds like you've done the immediate stuff by locking up and turning the boiler down. Folk have suggested emptying the fridge, good plan.
With regards to sorting the finances, if your mums affairs were quite straightforward I'd recommend doing the letters of administration/probate yourself, if you feel up to it. You'd need to do the majority of the legwork yourself anyway if you asked a solicitor to do it.
I'm a list maker so I had a big note book. In the front I wrote a page for each of the companies I needed to deal with eg gas, water, pension, council tax, car tax/car stuff, bank accounts, gp, club cards, window cleaner, everything. Get yourself comfy with a brew and just work through them all, making notes. At the back of the book was a brain dump/to-do list for stuff I kept remembering.
There's a really helpful guide another pp has linked, I found that really useful.
The undertaker was very kind and had lots of information leaflets for stuff. Lean on them of you need to.
And take care of yourself op. If you've done CPR for 30 mins you will be physically and emotionally exhausted as well as in shock and grieving. Eat little and often, drink plenty of water.