The time-travel lab has accepted a commission in order to help finance their research. While it may be impossible to bring items from the past through the net into the future (well, present from their POV), it is certainly possible to observe historic places in order to recreate them. The absurdly wealthy Lady Schrapnel wishes to rebuild Coventry Cathedral, exactly has it was immediately prior to the bombing in WWII. She has virtually taken over the time-travel lab in order to accomplish this, and refuses to take no as an answer. Ned Henry is in charge of attempting to locate something called the "Bishop's Bird Stump" which was in the cathedral in the weeks leading up to the bombing, but which disappeared at some point and cannot be located. It is of vital importance to Lady Schrapnel, as seeing the Bishop's Bird Stump in the original Coventry Cathedral was a turning point in the life of one of her ancestors - Tossie Mering - although the details are missing from the rather waterlogged diary which has survived. Verity Kindle has been sent back to Victorian England to attempt to peek at the diary before it gets ruined, and hopefully accompany Tossie on her trip to Coventry. On one of her trips she accidentally brings something forward through the net, which shouldn't be possible, and everyone fears that it will trigger a paradox and change the future - it seems that the change wouldn't be immediate, but that alternate timelines would slowly converge - giving people a little time to attempt to fix the problem. Ned has made so many trips to try and figure out what precisely has happened to the Bishop's Bird Stump that he has become severely time-lagged - and so he is sent back to the Victorian Era to get a couple weeks rest in the only place Lady Schrapnel will be unable to track him down. Ned becomes involved in Verity's attempts to fix the incongruity she may have caused and hilarity ensues.
As usual the details of the time-travel mechanics are slightly different from previous books. There is a much stronger focus on objects not being able to travel forward in time, to the extent that the characters have to ensure that the clothing they are wearing is from the future. There is mention of safeguards being built into the net to cause it to fail to open in the case of too much slippage - and yet based on the details given it always appears that slippage is something which gets calculated after the travel has taken place. It is also the case that people originally tried to bring treasures through the net, and were unable to, years prior to any safeguards being implemented, so it is very unclear exactly what is preventing objects from travelling forwards in time.
At any rate, if you're willing to overlook some incongruities, and accept that the universe has some sort of organizational principle which prevents certain types of paradoxes and contrives to repair itself in the case of minor damage, then the plot is quite entertaining. But the plot isn't the best thing here, that's definitely the characters and the Victorian setting. This is a story I will keep coming back to, but I think it is better to read it by itself.