Op - Hope you are doing ok. Since she owns the house, there is absolutely no rush to empty it
My DM died earlier this year, we did get estate agents out straight after the funeral, but only because DB didn't want to return to our home town anytime soon. Then it is up to the executors how quick to put it on market, and the house can be emptied whilst it is on market. Mums sold v fast but we then had 3 months for sale to go through, giving DH and I plenty of time to empty it.
Assuming she has a will, and depending on the complexity of her estate and who are executors, it is a fairly easy process to do Probate without professionals. My DB and I were joint executors, I did most of leg work, but it was straightforward, getting the value of bank accounts, life policies, value of house, value of any other possessions (v little in mums case!) - I posted the probate application within about 8 weeks of her death and we had the oath swearing about 3 wks after that. However, we did know what accounts and life policies she had, so didn't have to hunt for paperwork.
As others have said, gas and electric need to stay on. BT cut the phone off as soon as DB rang them, not a problem as no one there. When the death is registered there is an option to 'Tell everyone' which will basically let council tax, inland revenue, benefits/pension office etc know of the death automatically. Very useful as it saves ringing everyone. It can also include passport office and DVLA.