For example, The Cure's "Just Like Heaven" predominantly uses the chords A Major, E Major, B Minor, D Major.

A Major- F sharp, C sharp, G sharp
E Major- F sharp, C sharp, G sharp, D sharp
B Minor- F sharp, C sharp
D Major- F sharp, C sharp

It also uses the chords F sharp Minor and G.

I'm guessing it's in the key of B Minor (or D Major?), as I've been taught that lots of popular songs use this as it's easy to structure a song in this key on the guitar. But I don't know??!

Is there any easy-ish way of working out what key signature a piece is in?

Sorry if this thread has been made lots of times before!

thanks very much for your help,

Thanks very much for the link!

So, basically, I have to work backwards- using the chords I've got and seeing which key signature they all fit the formulae for? I think
Yes, that's basically the idea behind it. Sure, most songs aren't completely diatonic, but the link I provided gives a little hint in the right direction
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Thanks for your help again, I really do appreciate it.

With minor key signatures, do you have the song out using the chords in the relative major by using the instructions?

(sorry if i'm not making myself very clear!)
aside from looking at what chords and notes are used, you need to look at the resolution. where does the song feel like its leading? so in your example you figured its either B minor or D major. well, which one feels more like home? figuring that out is just as, if not more, important than just figuring out what key most of the notes and chords fall into. without knowing where the resolution is, its like having the map to go someplace but no address where to stop at. so just let your ear do the thinking once you figure out what basic key it is and it will find the root for you.