As others have stated, making any kind of living by writing songs exclusively is difficult bordering on impossible. It's a dwindling, dying profession, as the business has morphed over to labels primarily signing artists who write their own songs. I've been doing it for a living since the early 80s and have had a lot of songs recorded, but in the past decade/decade & 1/2, the cuts I've gotten have been almost exclusively songs I co-write with the artist who records them (or TV/film synch placements like Guitarhacker mentioned).

The first and most important thing you need to do if you're determined to pursue it is to educate yourself about the business. You don't "sell" songs - using that terminology to an industry professional is the equivalent of saying "I don't have a clue what I'm doing". Not knowing is okay, we all have been there at some point....but it means that you're not ready to submit your material yet.

I'd recommend doing two things. First, get a copy of a book called "All You Need To Know About The Music Business" by Donald Passman. I think the current edition is the 10th, and that's the one you want. You don't need to read it cover to cover, but you need to read the chapters on songwriting and music publishing. It was written for the U.S. market but most of it applies to the UK as well. At the very least you'll get a grasp of how the business works in regards to songwriting. Second, I would recommend researching and trying to find a songwriting organization in the UK to join. If one doesn't exist, you could join one in the U.S. (they take international members). A couple worth exploring would be SONA and NSAI. I would recommend NSAI (disclaimer- I'm biased, because I'm on it's BOD, but at least check it out for yourself).

Best of luck to you.

http://www.rogerbrownsongs.com
http://www.nashvillesongwriters.com/roger-brown