England is a part of the United Kingdom of Great Britain. The moment the Queen dies, her eldest son and heir, Charles, becomes King. There will be a Lying-in-State, a Ceremonial State Funeral, a time of mourning. About a year later, there will be a Coronation service, a blessing and anointing service of Charles.
Life will go on in the UK, the change in monarchs being seamless.
We do not know what the regnal name of Charles will be. He may choose to be Charles III or George VII.
Elizabeth is regnant of the UK, Northern Ireland, and fifteen other Commonwealth Realms; Charles assumes all of these roles.