There are two books here, the story of two children stranded in the past, and the story of scientists trying to get them home. The first is handled well, the second has problems.
Peter and Kate are in Kate's father's laboratory when they fall against what is supposed to be an experimental anti-gravity device and find themselves in England, in 1763. They are rescued by Gideon, once a cut-purse for a high class criminal, and now a steward. Gideon takes them to join the family he now works for, but when Gideon must leave to protect his brother (who has come under the sway of Gideon's old employer, Lord Luxon) the children also travel to London to try to retrieve the machine from the tar man.
Meanwhile back in the twenty first century, Kate's father is talking to Nasa about what might have happened and there is a country wide search for the children, complicated by the fact that their ghosts keep showing up.
Back in 1763 Kate and Peter have discovered they can "blur"into the future, but that they are always snapped back. This forces them to confess all to the Parson and the family they travel with: this is one of the things that makes the book work so well,. Having bitten that bullet and made a clear decision as to what can and can't be told, Buckley-Archer is in a position to use the fact of time travel rather than get hung up on the consequences although that haunts the book. Kate and Peter approach the problem logically, and eventually use their blurring technique to rescue Gideon from the scaffold.
If this entire book was set in the past I'd be recommending it as a picaresque--eighteenth century London is wonderfully depicted and I can forgive the coincident meetings--but the contemporary material lacks either the literary panache or the content confidence. First the writing of these sections is laboured and old fashioned. We are told what people feel, and furthermore, all the adults are simply role-holders. Peter's father is not a person. Neither is Kate's mother. The characterisation of the Parson and of Mrs.Byng in the eighteen century, even of the Detective Inspector in the twenty first, show that Buckley-Archer can write adults, but for some reason she has chosen to leave the contemporary parents as ciphers. This rather ties into the next issue, which is that Archer has committed the (for me) unforgiveable sin of children's literature paternas ex machina
. At first I thought this applied only to the dashing, if incomplete, rescue from the past by Kate's father at the end, but when I thought back I realised that although Peter and Kate leave clues for people, and aid Gideon in various ventures, actually, they are quite passive. The book is rightly titled because once you clear away the time-travel issue, this book is really about Gideon.
All of that said, I did enjoy it, but I think the right audience for this book is going to be nine or ten, whereas sorting out the characterisation of the parents would have given it greater appeal.