If you are a small charity and are investing less than a few thousand pounds in PR annually, it's probably not worth spending money on formal monitoring.
Most media organisations have a website, and will publish some (although not all) of their articles online. To keep track of these articles, set up a Google News Alert for your charity's name.
You can also measure the impact of coverage, for example, number of volunteers or donors recruited, or number of new visitors to your website.
If you are spending a significant sum on PR, it may be worth taking on a press clippings agency, who will monitor media for mentions of your charity. Press clippings services generally charge a "reading fee" of at least £50 per month and then charge a fee for each individual clipping.
There are a number of press clippings agencies to choose from including, Precise, Durrants and Cision. A full list of licensed media monitoring agencies is available here. Make sure they cover the media outlets you'll be approaching and find out the full costs.
There are various qualitative and quantitative analyses that clippings agencies can do on your coverage. For example, they can: assess the tone of coverage, calculate the "Advertising Cost Equivalent" of coverage and estimate how many people the article may have reached. Paperclip PCS has some useful information on different qualitative and quantitative evaluation techniques.