Wait, wait, wait... The label the original song was released on has NOTHING to do with this. The label owns the rights to the original recordings but not the songs as a composition. Those rights remain by the creator(s), which are the compositors and the lyricists.
It doesn't matter if you're giving it away for free or charge for it, but technically you can get in a whole lot more trouble if you made money from it. Not necessarily the bands/artists will get on your back but collecting societies, like ASCAP, GEMA or PRS for Music etc., will.
The legal situation is also from country to country (slightly) different and that makes things more complicated.
Technically, even putting up a cover on myspace can get you into trouble, because AFAIK, they don't have a "flat-rate agreement" with collecting societies. YouTube on the other hand does have this...
If you don't alter the composition/lyrics of the original track in any way for your cover, you might don't even have to contact the originators and ask for their permission to release it. But this is dependent on the exact legal situation in your country.
You're from the UK, aren't you? Then you will have to check with your collecting society, which is PRS for music, if you have to ask for the originators permission if you're making a 1:1 cover.
What you WILL have to do anyway if you want to rule out that the collecting society gets on your back, is to register your band and this track at the collecting society. This will make sure the originators (and you) are getting royalties and you're on the safe side. But it will cost money. If you register the EP as a whole than you will also receive royalties yourself if your own tracks are being played.
The whole thing with taking samples is another issue completely...