I am sorry to say this, but it is going to have to be replaced.
What your Kindle is doing is called an ink bleed. Once the ink has done that, it will cause your Kindle to do as you described.
Because it is more than a year old, you should contact Kindle. Sometimes they will replace it after the warranty, but that is at there discretion.
If they will not replace it, then they will sometimes give a discount on an upgrade.
I have had customers call and get a replacement after the warranty period.
Please contact Kindle UK at 0800 496 2449.
If you want to read your books on your computer in the mean time, please download the program here. - http://amzn.to/ZTF9ym
I apologize for this outcome.
If you have any questions, please reply and I will assist you.