Kat the Time Explorer by Emma Bradford, 1998.

Ten-year-old Kat is going to be living with her Aunt Jessie for the next year.  Her parents are botanists, and they are spending a year in South America, studying rain forest plants.  Aunt Jessie lives in a house in the same town as Kat and her parents so, by staying with her, Kat can continue going to the same school and see her friends.

Like Kat’s parents, Aunt Jessie is also a scientist and teaches physics at the same college where her parents teach when they’re not doing research abroad.  She inherited her house from their Great-Uncle Malcolm, who was an inventor.  Malcolm never invented anything that made much money or got much attention, but Jessie has been going through his things and discovered something interesting among his unfinished projects: a time machine.  The time machine seems to be nearly complete, although Jessie isn’t quite sure how to operate it or what should power it.  There is a drawing of a strange medallion in Malcolm’s notes, and Jessie found one with the same markings among Malcolm’s belongings, but it’s unclear whether this medallion is supposed to play any role in the time machine’s function or if it’s completely unrelated.

Then, Kat discovers another medallion in Malcolm’s old room, one with identical markings but made out of a different type of metal.  There is a space on the time machine for each of the medallions to fit.  When Kat experiments with how the medallions can fit into the machine, she activates it, transporting herself and Jessie back in time to England in 1851.

They find themselves on a train with other travelers heading to The Great Exhibition in London where people from around the world will be displaying new developments in industry and technology.  No one notices Jessie and Kat’s sudden arrival because the train is packed with people and the time machine has somehow altered their clothing and other small objects in their possession to ones that are appropriate to the period.  They also seem to be able to understand people speaking other languages neither of them knew before.  The time machine itself is packed into an ordinary-looking bag.  The two of them decide that they can’t use the time machine on the train where everyone will see them, and besides, they are both curious about the time they find themselves in.  After a temporary mix-up where they are separated at the train station, they find each other again and manage to locate a woman who will rent a room to them for a couple of days.

Unfortunately, when they start unpacking in their room, they discover that their bag was accidentally switched at the station for an identical one.  They no longer have the time machine and can’t get home!  Inside the bag they have, they find articles of men’s clothing, a small spring of some kind, an incomplete sketch of some kind of invention, a ticket to the Exhibition, and a letter written to someone named Edward from his brother Sidney about the Exhibition and the invention they plan to demonstrate there.  The brothers are very concerned about the success of their demonstration and are depending on results to make some money and save their family’s estate.  With those clues, Jessie and Kat must track down these inventors and find their time machine, saving not only themselves from being stuck in the past but the future of the two brothers!

There is an educational section in the back that explains about the Victorian Era and the Great Exposition.  It also discusses Victorian manners and tea parties.  There are tips for making little sandwiches of the kind people would eat at tea parties.

This book is part of the Stardust Classics series.