Camera Upgrade!

I have been pondering a camera and/or lens upgrade for some time. The main aim is to improve my wildlife photography.

I currently use a Canon 600D with a Tamron 18-270 lens attached; plus I have the EFS 18-55 lens that came with the camera.

I think I have settled on a 100-400 lens, but should I also consider a new camera body; and should it be a full frame model?

Are there any recommendations from blippers who have already taken an upgrade path? Thanks.