Where do you go if you want to write some technical documentation for a free and open source project?
If it is portfolio building you are after, then your best bet would be to join a project whose software you actually use. Join the user and developer email lists, start to provide sensible answers to user questions, and then start working on appropriate documentation. Many projects will use wikis for their documentation these days. They may require you to register in order to add content, but that is usually just to help prevent wiki-spam. More formal documentation writing needs to go through the project leader(s), but having demonstrated your skills on the user list (and possibly in a wiki) you will almost certainly receive a warm welcome.
Is there a brokering service specifically for technical writing?
I don't know of one yet. Please add one here if you know of one.
Is there a local project I could get involved in and help with documentation?
Probably the best route for this is to check in with your local Linux User Group in the UK http://www.lug.org.uk/ They might be able to use your help directly, or point you to a local project that could use your help.
Are there any other alternatives?
There are always other alternatives. Here are some (please add others):
UN Online Volunteering http://www.onlinevolunteering.org/ Not all projects involve free and open source software, but many do. You specify what your skills are and they help find you appropriate projects that could use your help. And yes, they do like people who can help write documentation.
this wiki itself could use your help
Some related OSS Watch documentation on this subject is: