Come Back, Lucy by Pamela Sykes (1977), published in the US as Mirror of Danger, is one I've been meaning to review for ages--it has an extremely loyal following of readers who were haunted by it, and was made into a television show that seems to have been equally popular.
Lucy has lived a very quiet childhood brought up by her extremely old-fashioned aunt--playing spillikins and croquet, educated at home, and generally out-of-step with modern (1970s) children. When her aunt dies, Lucy is sent off to relatives she has never met (an uncle and aunt with three children of their own) and finds herself in a completely alien environment. The house is noisy--full of popular music, and television, and arguing. It is old on the inside, but in the process of being modernized (personal shudder) inside. And Lucy has nothing whatsoever in common with her cousins, and doesn't even have a room of her own. She doesn't want to be there one single bit.
And her cousins don't know what to make of Lucy either--she makes no attempt to even try to see any good in them, and it's hard to be friendly with someone who clearly doesn't want to be friends.
Lucy, in her loneliness, goes up to the attic alone--a place where the past of the old house has been left undisturbed. And there she meets Alice, who brings her back in time to the 19th century to play. At first, Alice seems like the perfect friend. But every time Lucy goes back to the past, Alice shows more and more of her true character. Alice always gets what she wants, no matter if she has to lie or cheat to do so. And now Alice wants Lucy to stay with her forever....
It's a lovey psychological drama, as Lucy's perceptions, and those of the reader, change over the course of the book. Alice becomes increasingly unlikeable, and downright terrifying at the end, and her modern family grows increasingly more sympathetic. I simultaneously sympathized deeply with Lucy, while wanting, now and then, to shake her just tad. And I sympathized with her new family too, but really wanted to shake the parents, especially toward the beginning of the book! (Honestly, when you bring a grief-stricken child into your home, you should make some effort to cut down on outside obligations and pay particular attention to her, finding out what she likes and what would make her feel safe and at home. Humph.)
It's more ghost story in feel than it is time travel--although Lucy goes back in time to visit Alice, with some small issues of clothing discussed, Alice seems to be actually haunting Lucy (and to a lesser extent, others in the family). It's the relationship between the two girls, rather than going back to the past, that's central, so if you are looking for a trip to Victorian England, you might be disappointed.
But at any event, it's a spooky, character-driven page turner that sticks in the mind, and I can totally believe that if, like so many commenters on Goodreads, I had read it as a child, it would have knocked my socks off.
Especially recommended for reading at during the Christmas season, when the book takes place--it's shows a nice contrast between a proper old-fashioned Victorian-style Christmas and a bright modern 1970s one. (Poor Lucy's horror when she saw her new family's decorating style resonated with me!)
Thanks to the wonders of YouTube, you can watch the 1970s tv show based on this book in the comfort of your own home--here's the first episode.
(Thanks, Anamaria, for lending this one to me!)