Removing wash basin faucet help!

Everything I am reading online about removing and installing faucets pretty much goes on the lines of - inset faucet from above, tighten cap screw from below, connect lines and done. But the problem I am facing in removing the existing faucet is that it has a fat t-pipe below, so there is not way it can be pulled out from the top. (Pics below: top, bottom, front. Sorry about the inverted image, somehow the upload manager insists on displaying it as such even though it shows up fine on my PC). So there has to be some way to remove the top part - but how? I did remove a small piece from the top of the handle and remove a screw from inside, but that did nothing. Then I tried brute force, trying to force the level anti-clockwise. That broke off the left handle. Tried grabbing the left top part with pliers and rotating but the grip is not sufficient. So what is the trick here? How do I remove this faucet? Thanks in advance for the help.