Technically yes, but if they can’t form a government the King can and will call an election.
I think there is a very high chance they will be unable to agree on a new leader and will therefor be unable to form a government. Even if they do elect a new leader, if that leader can barely control the party that would not a functioning government, and they should call an election.
At some point Tory MPs need to grow some, call an election, and except that it may mean loosing their job.
By "the continent" I assume you are speaking about the rest of europe, and in that case I don't think you can say anything coherent about their systems.
I think there is a very high chance they will be unable to agree on a new leader and will therefor be unable to form a government. Even if they do elect a new leader, if that leader can barely control the party that would not a functioning government, and they should call an election.
At some point Tory MPs need to grow some, call an election, and except that it may mean loosing their job.