The "T" handle slips over the top of the shaft and if you look underneath the black plastic you will see a tiny inset bolt with allen key slot that you need to tighten down to make it stay in place.The black plastic cap is held on with a clip but if cracked or broken underneath will make it flop off.If the threaded insert is buggered it (chrome handle) will twist/spin around
Is this the "T" you speak of?
Ebay item 4601600561

David