Where can I find a list of all UK _full_ postcodes including street name and their precise coordinates?

The Royal Mail is the supplier of the 'official' Post Code database for the UK - they own the postcodes and postcode to GIS mapping. It's copyrighted and has some significant license fees.

Postzon is the product they sell to link the postcodes to the GIS co-ordinates.

There have been third party providers from outside europe who released details in the past for a fraction of the costs, but it's a very grey area, and you are then in consult a lawyer territory.

The OS "free" version is useful, but it does have a few limitations, for example no data for Northern Ireland, the Isle of Man, Guernsey or Jersey.

I vote for Doogal's version with the extra latitude and longitude data, which is more useful for geo-mapping like OpenLayer.