If you have partners or are part of a larger organisation, ask them to link to your charity's site, preferably using your key phrase as anchor text. Ask supporters, volunteers and employees of your charity if they have a website and could link to your website.
Get your charity or social enterprise added to business, local area and category-related directories. One of the biggest web directories is dmoz. A lot of other websites (eg. Google Directory) are based on dmoz. Yahoo also has a big directory. It charges an annual fee to list commercial organisations, but will add non-commercial sites free of charge.
Here is information I have compiled on other types of website directories.