I'm sorry to learn of your loss.
Very likely you can contact the Registrar for the area of death online, as soon as it opens, and supply the details you have of the deceased, such as DOB, DOD, name, address, place of death, etc. They should give you a reference number. This will help when you go to make the appointment.
In order to register the death you need the Medical Certificate of Cause of Death from the hospital or attending doctor. There may be a delay in obtaining this, specially over a Bank Holiday period.
This is where having made initial contact with the Registrar's office is helpful as, strictly speaking, you must, by law, register a death within 5 days, not working days, but actual 24 hour periods. This is scarier than it sounds, specially if you are already upset by the death. In fact, you are at the mercy of whoever issues the Cause of Death certificate, and IME, a doctor doesn't rush back from a couple of weeks holiday to do so. But if you've informed the Registrar's office, you can relax knowing you've demonstrably done what you can. I can find no indication of anyone, ever, being prosecuted for late notification of a death, but the regulation can worry an emotional bereaved person.
Once you've managed to make an appointment and registered the death, you will get a free certificate allowing cremation or burial ('green form'), which you need to give to the funeral director to give to the crematorium or burial authority. You will also get a Death Certificate (about £11, I think). It's good advice to get plenty of Death Certificates at the time of registering the death. They are cheaper then and much less hassle than going back to a place of sad memories to get more.
Using a funeral director makes everything much easier as they can deal with all the authorisations and fees. They will also know how busy the local crematoria are, or who to contact about a burial. In some places the soonest cremation can be several weeks away, others, days. But a bit of a delay gives you time to spread the word around anyone you think might want to attend. The funeral director will be able to suggest celebrants and suitable places for a wake if you need that.
One of the hardest things is assessing how many people will come to the funeral, specially for a younger (more living friends) or particularly sociable person who died. You may want to have a service sheet printed and/or provide refreshments at a wake and try to judge how many. Again, from experience (I hugely underestimated!), people are happy to share sheets and a decent venue will understand and whistle up more sandwiches or at least more tea and coffee, if necessary.