Based on the TeamCity documentation I can see that it is possible to trigger a build over http:
http://confluence.jetbrains.com/display/TCD7/Accessing+Server+by+HTTP
For example,
http://testuser:testpassword@teamcity.jetbrains.com/httpAuth/action.html?add2Queue=bt10
However, I need to force a build to also rebuild certain dependencies when it is added to the queue. Is this possible?