I sometimes crave solitude, but that's entirely different - what you're experiencing are the pangs of loneliness, and you are one of an increasingly large minority.
There's no magic formula for finding a companion, and it's often said that the harder you try the less likely you are to be successful. One of the problems with dating services is that they introduce you to people with whom you may have little in common - apart from the fact that you're all looking for relationships. Real-life encounters tend to happen when two people are naturally in the same place for the same reason - they start off from the basis of at least one common interest.
Are you a gregarious person - someone who mixes well? If you are, and you have interests, you might try joining clubs or associations. If you enjoy being out and about you could do a lot worse than the Ramblers Association click here you would meet others who are unattached, and the fact of having a joint interest can work wonders.
There are all kinds of organisations, and if you have hobbies or just casual interests there's bound to be one that would fit the bill.
Good luck, often you find what you're looking for when you least expect it, but to do so you'll have to be out there, meeting people in everyday situations.