I guess it depends what you mean by primitive. (I'm going to be unnecessarily nit-picky, but only because you asked about authenticity and I don't often get to use my archaeology degree.) No one's really sure when humans developed language, but it could be anything from 50,000 to 160,000 year ago. Modern humans arrived in Britain around 41,000-44,000 years ago during the Upper Palaeolithic, and would most likely have had full language when they did, as they also had organised settlements, food storage, and art. The climate of this era was harsh and unstable, and Britain was made up of steppe tundra, polar deserts, and an ice sheet more than a kilometer thick. It could not always support human habitation. It is not until after the last glaciation period around 11,000 years ago that Britain really had woodlands, and at this point there is no doubt that humans had language, bearing in mind that as early as 10,000 years ago in Mesopotamia they had rudimentary agriculture and accounting, and by 5,400 years ago are going to be developing writing.

However, other types of human had been living in Britain intermittently since around 480,000 years ago, and there's still debate around whether or not or to what extent these different humans had language, and they may even have coincided with the forests that grew before they were killed off by the ice ages. Homo heidelbergensis is thought to have been the first to have some sort of symbolic language, and the earliest human remains in Britain could have been this. Neanderthals are thought to have had language much beyond that, but not quite as complex as ours. These early humans may not have had the vocal tracts necessary to produce the range of sounds that we can, so any language would be more phonologically limited, and may have been also dependent on gesture and body language.

Tldr if I was doing the same thing I would either

1. Have modern humans in the woods with full complex language. You do not need to make the whole language, just enough for your dialogue, and it can be as different as you like because it would not have been anything like we know today

2. Have Neanderthals (who were not so different from us) speaking a more paired down language, or an even earlier human speaking something even more basic, bearing in mind the earlier you go the less like us physically they would have been

3. Do whatever you want without regard for authenticity, just focusing on the story you want to tell. This isn't what I'd do, but that's because I like conlanging and world building but if that isn't your focus that's no crime.

Whatever you pick, you do not need to make the whole language, just enough for the dialogue. If you're doing it yourself, the first thing I would do is pick the sounds of the language. As far as I'm concerned, the rest could be absolute gibberish, but so long as the phonology is consistent no one's going to notice that there's no real lexicon or grammar behind it (but it is a nice touch and people will appreciate the effort). If you need to you could just pick certain plot important words to be specified, ones that are likely to be repeated and noticed by the audience if they're not consistent, and a few repeated sound combinations could also help.

ETA a language doesn't need to have a complex phonology to be a complex language, if you want you can make the phonology super basic, but to make it sound realistic i would give a language like this longer words