If you're interested in prehistory (which I would note, falls outside the realm of "historical archaeology") then a degree in "just" archaeology (combined with another subject or not) may be more aligned to your interests, as you will approach both prehistoric and historical archaeology. In terms of "ancient history outside of classical history" then that really is encompassed either by archaeology or really the realm of regional studies/language degrees in the relevant language(s) (or sometimes in religious studies, depending on the regiona/area and age of "history" being considered), more than a course in ancient history. Alternately a degree in archaeology and anthropology may also incorporate aspects of ancient cultures on both sides, although this is less the case with the anthropology side of the course at most unis (which typically will focus on more modern cultures via social anthropology, or prehistoric humans via biological anthropology); the Oxford A&A course integrates the modern and ancient sides a bit more than many I think.
Outside of that and more in the "classical" realm, a few programmes might allow you a broader scope for exploration of the history and archaeology of both classical and other comparable ancient civilisations, but they are somewhat few. The Ancient World programme at UCL or Classics & Oriental Studies at Oxford, for example, both may allow you more leeway in that regard. However Classics & Oriental Studies at Oxford is going to be a lot more language/text based than archaeological (although you may take archaeology options and archaeological material may also inform some of the non-archaeological papers. The ancient world programme does offer some scope to explore the prehistoric elements as well through external optional modules (which you can only take a limited number of but they are there as an option!), along with one module on the prehistory of Europe specifically which is considered an "in programme" module that you can take freely.
Something that may also be of interest would be the history of art, as some courses may also extend that to archaeological material or potentially even prehistoric art (e.g. rock art), and although often the courses are Euro-centric there will typically be at least some (and sometimes much) non-European art/archaeology considered. The course at SOAS for example is fairly non-European in character and as a result also distinguishes less between "art" and "archaeology". There is also a joint course between SOAS and UCL if you wanted to incorporate more European (including classical) art. You would also normally situate the art (or archaeological objects) in their historical context and thus be learning about the history of the period to some extent. However it would probably not include much if any practical skills in archaeology which may limit you in terms of becoming a professional archaeologist (although perhaps e.g. an archaeology degree followed by history of art masters might let you then balance the archaeological elements with the most historical matters, across a range of cultures).