You can take your iPhone, iPad, or eligible smartphone to an Apple Retail Store and get immediate credit toward the purchase of a new device. Alternatively, you can get an online estimate for your device. If it qualifies, you would mail it in and get a credit for its value.
For the U.K., Apple is accept smartphones manufactured by Sony, Samsung, Nokia, LG, HTC, and BlackBerry.
As a reminder, before the release of the iPhone 6, Amazon was found to offer the highest price for your used iPhone. It may be prudent to shop you old device around before trading it in.