The subject of "government" is usually called (or subsumed by) the term "politics" in the UK. There are innumerable departments of politics in the UK, many of which have research in comparative government etc. The PhD in politics at LSE is actually offered by the department of government there, and their politics programmes were known, unitl about a year ago, as "government" (e.g. PhD in government, BSc/MSc in government, etc).
Generally speaking, the "name" of the PhD is pretty much irrelevant compared to the content of the associated PhD project, and/or what research the department through which you will be supervised for the PhD specialises in. The PhD is just a "shell" for your own research, which may be in some area which could be called government, or anything else - whether you do this in a department called "government" or one called "politics" wouldn't make a difference to the actual research you're doing provided there is a supervisor able to supervise you on that area.
In short, just look at politics departments and identify which faculty do research in the area you are interested in (presumably comparative government). I would note if your area of interest is actually in political theory you may want to look at possible some philosophy departments specialising in political philosophy as well.