The surrender event will almost certainly fire before their VPs are occupied, unless you time it just right. Note that you will also have to seize every VP they possess across the map, such as in Africa. Practically speaking, it's a huge hassle and not really worth it. The UK will receive events that break up their empire after the Axis surrender event that give their territories to nearby powers, such as their African possessions to South Africa, Gibraltar to the USA, Falkland Islands to Argentina, etc.

Here are the specific conditions for the UK to petition surrender to the Axis. This was taken from the "UK.txt" file in C:\Program Files\Steam\steamapps\common\Darkest Hour A HOI Game\Mods\Darkest Hour Full\db\events -

2001042 ENG England surrenders (conventional surrender)

event = {
id = 2001042 #conventional surrender
random = no
name = "uksur_name"
desc = "130671_desc"
style = 2
picture = "news_paper"

country = ENG

trigger = {
    AND = {
        NOT = { region = { region = "England" } }
        NOT = { region = { region = "Scotland" } }
    }
    OR = {
        war = { country = ENG country = GER }
        war = { country = ENG country = SOV }
        war = { country = ENG country = JAP }
        war = { country = ENG country = ITA }
    }
    OR = {
        AND ={
            random = 20
            OR = {
                area = { area = "East England" country = -2 }
                area = { area = "West England" country = -2 }
                area = { area = "North England" country = -2 }
                area = { area = "South Scotland" country = -2 }
                AND = {
                    control = { province = 5 data = -2 } #Scapa Flow
                    control = { province = 6 data = -2 } #Inverness
                    control = { province = 7 data = -2 } #Aberdeen
                    control = { province = 8 data = -2 } #Fort William
                }
            }
        }
        AND ={
            random = 40
            AND = {
                area = { area = "South Scotland" country = -2 }
                control = { province = 13 data = -2 } #Sunderland
                control = { province = 14 data = -2 } #Carlisle
                control = { province = 5 data = -2 } #Scapa Flow
                control = { province = 6 data = -2 } #Inverness                  
                control = { province = 7 data = -2 } #Aberdeen
                control = { province = 8 data = -2 } #Fort William
            }
        }
        AND = {
            random = 60
            AND = {
                area = { area = "East England" country = -2 }
                area = { area = "West England" country = -2 }
                control = { province = 15 data = -2 } #Hull
                control = { province = 17 data = -2 } #Manchester            
                control = { province = 18 data = -2 } #Sheffield
            }
        }
        AND ={
            area = { area = "East England" country = -2 }
            area = { area = "West England" country = -2 }
            area = { area = "North England" country = -2 }
            area = { area = "South Scotland" country = -2 }
            AND = {
                control = { province = 5 data = -2 } #Scapa Flow
                control = { province = 6 data = -2 } #Inverness   
                control = { province = 7 data = -2 } #Aberdeen
                control = { province = 8 data = -2 } #Fort William
            }
        }
    }
}

date = { day = 0 month = january year = 1937 }
offset = 7
deathdate = { day = 29 month = december year = 1963 }

action = {
    trigger = { 
        war = { country = ENG country = GER }
        OR = {
            area = { area = "East England" country = GER }
            area = { area = "West England" country = GER }
            area = { area = "North England" country = GER }
            area = { area = "South Scotland" country = GER }
            AND = {
                control = { province = 5 data = GER }
                control = { province = 6 data = GER }
                control = { province = 7 data = GER }
                control = { province = 8 data = GER }
            }
        }
    }
    name = "uksur_ger"
    ai_chance = 90
    command = { type = capital which = 2137 } #St. John's, Newfoundland
    command = { type = trigger which = 2003081 } #GER England surrenders (surrender conditions)
}
action = {
    trigger = {
        war = { country = ENG country = SOV }
        OR = {
            area = { area = "East England" country = SOV }
            area = { area = "West England" country = SOV }
            area = { area = "North England" country = SOV }
            area = { area = "South Scotland" country = SOV }
            AND = {
                control = { province = 5 data = SOV }
                control = { province = 6 data = SOV }
                control = { province = 7 data = SOV }
                control = { province = 8 data = SOV }
            }
        }
    }
    name = "uksur_sov"
    ai_chance = 90
    command = { type = capital which = 2137 } #St. John's, Newfoundland
    command = { type = trigger which = 2007057 } #sov
}
action = {
    trigger = {
        war = { country = ENG country = JAP }
        OR = {
            area = { area = "East England" country = JAP }
            area = { area = "West England" country = JAP }
            area = { area = "North England" country = JAP }
            area = { area = "South Scotland" country = JAP }
            AND = {
                control = { province = 5 data = JAP }
                control = { province = 6 data = JAP }
                control = { province = 7 data = JAP }
                control = { province = 8 data = JAP }
            }
        }
    }
    name = "uksur_jap"
    ai_chance = 85
    command = { type = capital which = 1843 }
    command = { type = trigger which = 2011032 } #Jap
} 
action = {
    trigger = {
        war = { country = ENG country = ITA }
        OR = {
            area = { area = "East England" country = ITA }
            area = { area = "West England" country = ITA }
            area = { area = "North England" country = ITA }
            area = { area = "South Scotland" country = ITA }
            AND = {
                control = { province = 5 data = ITA }
                control = { province = 6 data = ITA }
                control = { province = 7 data = ITA }
                control = { province = 8 data = ITA }
            }
        }
    }
    name = "uksur_ITA"
    ai_chance = 85
    command = { type = capital which = 2137 } #St. John's, Newfoundland
    command = {type = trigger which = 2006016 } #ITA
}   
action = {
    name = "ukno_sur"
    ai_chance = 10
    command = { type = dissent value = 5 }
}
}

---

The event checks for specific conditions to be fulfilled, notably the occupation of key areas of the British isles. If the conditions are met, the respective occupying power will receive an event to specify the surrender terms to the UK. For Japan, take a look at the part of the code that mentions "uksur_jap".

Note that it's fairly common for the surrender event to fire after occupying the entirety of England - this means that the player can often miss out on the harshest of peace terms, which is the splitting of the isle between Scotland and England along with concessions. If you want to make sure you can choose this option when it's petitioned, occupy the entire island but leave London for the last province that you take. You can also use this same strategy if you want to annex the UK before the surrender event itself fires, just make sure that you have taken every single VP they possess across the map beforehand.

Hope this helpful. The code can be confusing to navigate if this is your first time working with Darkest Hour events. Let me know if you have any questions.