Anthropology vs History

Archaeology is distinct from anthropology, although the two inform each other. In the UK "anthropology" normally refers to "social (or cultural) anthropology", although biological (or physical) anthropology also exists and in many ways connects anthropology more practically to archaeology. Biological anthropology is sometimes framed as evolutionary anthropology or human sciences as well. Typically in the UK a degree called "anthropology" will be a social anthropology course.

Social anthropology is broadly the study of human culture and society, focusing much more culture than sociology does, and employing it's own method of inquiry and publication, namely ethnography. Historically (social) anthropology has focused on the study of "other" cultures, i.e. non-western cultures (again, compared to sociology which historically tended to focus on western society) although modern anthropology addresses the problematic nature of "othering" non-western cultures and increasingly adopts e.g. postcolonial approaches to the study of non-western cultures, and also uses the same tools to explore aspects of western and emerging (e.g. digital) culture(s).

Essentially, it's not really that much like history, although anthropological approaches (and in places, sources) can be applied to historical research. If you are (potentially) interested in (social) anthropology I would suggest you look at some ethnographies of various regions or themes of interest to you. There are many possibilities and I'm sure your local library may be able to offer some suggestions. Goldsmiths has a joint honours course in History and Anthropology, and Oxford allows you to study anthropological approaches to history in one of the prelims papers they offer. You may also be able to take anthropology optional modules in a history degree if they offer them, or vice versa (e.g. at LSE).

Archaeology relates to history in the sense they both primarily study the past, however archaeology, as you note, focuses more on material culture and artefacts, whereas history tends to focus more on textual sources. However textual sources are relevant and of interest to archaeologists, and material/archaeological evidence is of relevance and interest to (some) historians. So the two aren't wholly separate disciplines, and in some courses the line is more blurred than others (e.g. in most ancient history courses archaeological material is quite relevant, and even in most general history courses that include options in medieval history archaeological material is also well within the realm of possibility for considerations as historical source material).

Both degrees are as "respectable" as the university offering the course, and the relevance of that "respectability" (or perhaps "prestige") to graduate prospects is approximately the same for most graduate roles outside of investment banking i.e. not very. Someone who studied anthropology (and/or archaeology) or history will be just as well placed in the job market as each other and indeed anyone that studied any degree and are applying to non-specialist grad roles (i.e. the majority of them).

The major factor in such job-seeking will be how well the job-seeker used their time at university (or rather, between terms) to undertake relevant work experience/placements/internships/etc, and how effectively they can communicate and demonstrate the relevance of the transferable skills earned in the degree to the workplace (the transferable skills in each degree are more or less the same).