A friend of mine did her Masters in International Relations at Sussex after having done her BA in Humanities, so it can be done with a degree in English & Philosophy - it all depends on which Uni you want to apply to, and what they require for entry onto their MA degree.
Best thing to do is make a list of universities (where you want to do that MA), and then check their MA International Relations course details online at their website, they will often state the requirements there.
Failing that, email the department's postgrad officer and ask if your BA allows you entry onto their MA in International Relations. They are generally very helpful & respond quite quickly.
Good luck!