The value of a small number of shares may make it uneconomical to sell them so you can give them to charity through ShareGift, the charity share donation scheme.
This is a registered charity (no.1052686) which accumulates small shareholdings, sells them and donates the proceeds to a wide range of different UK charities.
The service is free (although there may be an indemnity fee if you have lost your share certificate).
Giving shares to charity in this way does not give rise to any gain or loss for Capital Gains Tax purposes, and UK taxpayers may be able to claim income tax relief on the value of your donation.

For further information visit the ShareGift website at:
http://www.sharegift.org
or call them on 020 7930 3737