Decades ago, I read a story where a boy and girl slipped back in time to the Roman days in England. It was the first time travel story I read and fascinated me. The kids knew they were speaking English but it was coming out as Latin. They learned about Roman life in Britain. Can't remember what adventures they had.
This sounds like Puck of Pook's Hill by Rudyard Kipling. The book contains a series of linked stories about the adventures of two children across different times in England's history, guided by a magical elf. One of the stories definitely has an encounter with a Roman soldier which leaves the children impressed by the similarities between the Roman and English lifestyles. The awareness of communication across languages and culture are also explicitly mentioned. Given that this book was originally published in 1906, it is possible for you to have read it decades ago.
You can find a free version on Project Gutenberg: https://www.gutenberg.org/ebooks/557 (original) and https://www.gutenberg.org/ebooks/15976/ (illustrated). The Roman portion starts on page 137 with the poem A Centurion of the Thirtieth, followed by the eponymous story, A British-Roman Song (A.D. 406), On the Great Wall, A Song to Mithras, The Winged Hats, A Pict Song.
Perhaps some of H.R. Millar's illustrations will strike a memory:
This is likely only a partial match.
Could this be The Magic Treehouse #13: vacation under the volcano?
In this story, the protagonists Jack and his sister Annie are taken to ancient Pompeii, just before the eruption of Mt Vesuvius in AD 79. I think they have to find an ancient library before it is destroyed by the pyroclastic flow from the eruption. Generally in these stories, the protagonists are given the magical ability to communicate with those in whatever era they are visiting.
I know this isn't in England, and The Magic Treehouse is actually based in the USA
A bit of a long shot as it does sound like you are talking about a straight-up story, but it couldn't possibly be a puzzle book at all?
Time Train to Ancient Rome, by Gaby Waters (Part of the Usborne Puzzle Adventure Series) bears a number of similarities to your description, though admittedly transports the protagonists to Rome itself rather than Roman Britain. I seem to recall a scene involving the language coming out as Latin as mentioned, although it has probably been two decades since I read it myself!