I read this time travel story some time in the 1970s. The story started in what was then the modern day with three young people, (two boys and a girl) committing some sort of crime against an old woman. That whatever they did was wrong was not soft-pedalled, but the three protagonists were juvenile delinquents rather than hardened criminals. The woman turns out to have supernatural powers and punishes them by sending them back in time to 12th century England. If I remember rightly they "wake up" in the bodies of three young people from that era, and to redeem themselves they have to save the proper inhabitants of those bodies from various bad fates. (I cannot remember whether the 12th century people were sent forward in time or were just in some sort of limbo while the story happens.) The girl is either being forced into marriage or into becoming a nun. I can't remember what the two boys had to do, but one of them ends up fighting in the crusades. I think the other boy was thrown into a position where he was involved in political intrigue, possibly as a clerk in the service of King Henry II.
I recall the book as doing a good job of portraying the people of that era as more brutal than people in late twentieth century Britain, but also as having virtues that modern people lack.
One scene that stood out was when one of the twentieth-century characters is watching Henry II perform public penance at Canterbury for instigating the murder of Thomas à Becket. The watcher thinks of Henry as a man ahead of his time, and expects to see some sign of him performing his penance (to be stripped of his fine clothes and publicly whipped by the monks of Canterbury) as a canny political gesture, even if it did also involve some genuine penitence. But when the watcher takes one look at Henry's face, he realises that he was wrong. Henry truly believes.
In the end the three main characters do manage to save their twelth-century equivalents, redeeming themselves in the process, and are able to return to their own time.
