Sorry for your loss. I have been through the deaths of my DH (sudden, very young), my sister (cancer, also far too young) and most recently my father (elderly, multiple causes, an expected death).
Most importantly, look after yourself, eat properly, accept help and don't hesitate to ask for actual specific help if you need it. Loads of people will say 'if you need anything, just ask' but they won't proactively offer anything specific. So if you need childcare on a specific day, or someone to sit with you while you deal with the horrible tasks of choosing a coffin, or help drawing up lists of people to notify, or just can't face cleaning the bathroom, ask someone. People usually feel good about helping out but aren't sure what to offer to do.
As far as practicalities go, if you had a year of dealing with cancer, did you have time to sort things out in advance like getting accounts into joint names? If not, switching things like utility bills into your name is probably the first thing you will have to do once the funeral is over. Funeral directors will help you with things like newspaper announcements or suggesting charity donations for friends if you want them.
How old are your DC? Winston's Wish has great advice on how to help children through this. I think some hospices and cancer charities also have help lines and services for children.
The 'tell us once' service is very easy to use once you have a death certificate. For everything not covered by that, try googling the name of the utility/insurance companies/pension providers/bank etc plus 'bereavement' and you should find they have a dedicated number for you to call, or just forms on the website you can fill in rather than having to explain yourself to call centres every time.
You may be able to handle probate yourself, but it is definitely worth at least talking to a solicitor first before you embark on it - there are various levels of service they can provide, from doing everything (expensive) to just helping you format information and submitting the probate forms.