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The evidence that you would produce would vary to some extent on which particular group you belonged to (eg. whether you were gay or belonged to a political party). It would ideally be things specific to you such as evidence that you had been attacked or pursued by persons wishing to persecute or cause you harm because of your membership to that group.
Supporting literature of the general attitude to your social group is helpful but not conclusive. You can obtain specific information to your particular country by consulting the following UKBA specific country guide:-
If you are unsuccessful in your asylum claim and you can't appeal to a higher court then I am afraid that you would be deported almost immediately.
The 14 year length is law, a solicitor can help you prove your case is within the law but they will not be able to reduce the required length of time.
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