You used to be able to register copyrights at Stationers' Hall in London but alas they have discontinued this service; and when I spoke to them (about a year ago)they could suggest no other alternative for proving copyright. Someone please correct me if I'm wrong or out of date on this. I repeatedly read advice in the trade mags that you should NOT pay money to one of those commercial services that offers to register this for you, because (if they are honest) they are only doing what you can do yourself for free; and if they are dishonest it doesn't bear thinking about. Either way, how are you going to ever know for sure? I have no personal experience of these places but I'd steer clear of them.
You might consider mailing yourself two copies rather than one, and keep them in separate places. Also make sure to send them registered post with the date clearly visible, so there's official written proof of posting. I no longer live in the UK but when I did I remember being told by a post office worker that I must not seal the envelope with tape or any external fastener because doing this can obscure the fact that it could have been subsequently opened and re-sealed, thus making your case harder to prove. This means that your only proof rests upon the clarity of the date stamp (sometimes these smudge so ask them to stamp it again if it's not clear on the envelope itself - I don't know how long they keep their receipt books) and the strength of the glue holding down the flap. I always reinforced this with a bit of household glue (or Superglue if you're feeling paranoid) and then put a couple of books or some heavy weight on it for awhile to stick it down good. (Of course, being smarter than me, you don't need to be reminded not to Superglue the book to your letter... no, didn't think so...)
The post office clerk also had me write my signature across the join where the envelope flap and the main part of the envelope meet, as further proof that it had not ever been tampered with, and I also wrote it across the other seams. And of course remember not to open anything, hang onto the receipts, store them in a safe place, and it's a good idea to write on the outside of the envelope what the song titles are because it's so easy to forget and mix things up; and if you open the wrong one you've destroyed your date proof. As an extra measure I always put my signature on the copies inside, though I haven't heard that this is necessary. Be sure to affix the copyright symbol (the little C inside a circle), the year, and your first & last names on the song itself (not on the outside of the envelope where it's visible to all!) because it USED to be that you could permanently lose the copyright if you neglected to do this. They've changed that rule now, but you'd still better put it in. If it were me, I would do this in my own handwriting rather than typing so the name constitutes a signature (told you I was paranoid).
If anyone knows a better method than this, I'd be very interested to hear it too. Best of luck, Bonnie