STORY OF THE AMULET

At the end of Five Children and It Robert, Anthea, Cyril, and Jane promised not to ask the Psammead for another wish as long as they lived, but expressed a half wish to see it again some time. The children are reunited with the Psammead in a London pet store; the Psammead can't grant their wishes anymore - not after the last adventure - but he does tell them where to find half of an amulet of great power.
The ancient Amulet can grant them their heart's desire and journey through time. The children desire the return of their parents, and their magic adventures start over again with a journey through time to ancient Babylon, Egypt, and Atlantis.

The trilogy of Five Children and It, The Phoenix and the Carpet and The Story of the Amulet.