I hope it's possible because this is what I intend to do. As already stated above, many universities in the UK as well as continental Europe, I might add, require "only" an undergraduate degree in a "related" field.
Unfortuenately, some universities interpret "related" as "really damn closely" related, in fact, related usually - at least in my experience - means, 60 - 90 Credits have to be in the same courses (1). Additionally, some want to see a further amount of Credits in "related" courses (2) and/or a clear concentration on a topic (3), that is somehow related to you intended master course.
Let me give an example.
Assuming somebody studies history and wants to get into a politics master:
1. You would have to complete at least 60 Credit points worth of basic politics courses, which are usually not covered in a history degree, i.e. theory of democracy, political theory, international relations theory, theory of democracy etc.
2. "Related Courses" would be, for example, history of political thought (albeit there are scholars who think history of political thought has nothing to do with the science of history), history of international relations, history of party xy etc.
3. Even in not "related" courses you can concentrate (as long as the teacher leaves you a choice) on certain topics. So you are doing the seminar on the French Revolution? Then instead of tracing "battles" and crimes, trying to figure out the motives of the people or discussing whether the revolution is the beginning of a new age - all though pretty much all of those questions have political implications - you could concentrate on a concrete political science topic, employing political theory or tracing changes in the way people thought about politics.
To some my text might seem as kind of obvious. But really, when I started my "journey" in uni I didn't think it would have such a great impact, the courses I choose and the topics I have to deal with, that it.
So if it comes to the question whether its possible or not to get into a Masters program different from your Bachelor, I think it is possible depending on whether you started following a certain path from very early into your undergraduate degree and/or on the admission policy of the graduate institute in question. From my experience, naturally, universities with less applicants tend to be more flexible in regard to such a change of subject.
On a sidenote though, there are quite a lot of Master programes that are designed for undergrads from diffrent subjects, such as math/ business/economics for engineers, philosophy/ethics/law for economists or regional studies for busines undergrads and so on.