Please, I have a 6 month leave to enter and when I arrived, I've showed a return ticket for the next week. Now I'd like to stay for 15 days more. Should I inform that to autorities? Thank you very much.
You’re allowed to stay until the time you were given upon entry, usually six months. You do not have to notify immigration.
Note however that changing your duration of stay significantly can make you appear unreliable or dishonest and subsequent visa applications may be denied.
If it is your first visit to the United Kingdom, it is better to stick to that duration you gave them officially. They are even sometimes denying people visa renewals for staying shorter than they indicated in their visa applications.