The only source for BA award inventory are airline websites, such as BA.com. There are some services that screen scrape BA.com and offer the award data, some charge for that free data, and some offer it for free. Here is a good list of such tools: http://www.flyertalk.com/forum/18254612-post2.html

Of note are:
- www.Awardnexus.com which covers all 3 alliances and has a free version for FT members. The paid version has automatic award checking and alerting
- www.awardtravelr.com which covers all 3 alliances and is totally free