Yes, the British monarchy will of course survive the Queen's death - and this is why:
Republicanism in the UK remains among the lowest in the world, with figures rarely exceeding 20% in support of a British republic, some polls have it as low 13%, and consistent 70/80% support for the continuation of the Monarchy.
To abolish the British monarchy will be very difficult.
1: Most polls must show a majority for a republic, this is very very unlikely.
2: Majority in the house of commons for a referendum, this is not going to happen.
3: Majority in the referendum for a republic, this is not going to happen.
4: Changing the country's name, changing the pound, remove the royal name from all state institutions. These are just some of the things that must be changed.
5: All of this is going to cost so much money that even many Republicans will start doubting it.
6: The vast majority of the british population will never vote to replace a constitutional monarchy with a divisive politician or a celebrity.
But will it be a challenge for the monarchy to lose the most popular, famous and most iconic head of state (many would say person) in the world? Yes of course it will. And I think (like some of the more serious commentators) that this will be the biggest challenge the British monarchy has been facing since 1936 (much bigger than Dianas death).
The British Monarch is also head of state of 15 other nations and (for now) head of the commonwealth - will that continue after the Queen?
Canada: Most likely.
Australia: 50% yes - 50% no.
New Zealand: Most likely (at least for a while.)
The 12 other countries: Don't need (or choose not to have) referendums - so it's easier to abolish the monarchy for them.
I thought in 2012 that some of these countries would become republics by 2017, but it has been postponed again and again and again.
And if these countries choose to elect their own head of states, then it has nothing to do with republicanism - it has more to do with the idea of having a foreign person as their head of state.