/// A popular story says that the arch was moved because it was too narrow for the Queen's state coach to pass through, but, in fact, the gold state coach passed under it during Elizabeth II's coronation in 1953.Wiki///
but I also found out that the real reason was there was no room for it when the palace was enlarged - so in fact it was too BIG for the palace.
However, I guessed that the setter of the quiz was going by the popular story. One way or the other it was built for the palace but ended up at top of Park Lane.