I found an app on the Xperia T forums that allows playback of the FM Radio without a headset attached.
There are three versions.
- The Original from the Xperia Z (with the Visualizer)
- The Jelly Bean version (same as the Z but without the Visualizer)
- The ICS version (the old one that came with the ICS Update)
Tip: Placing a metal close to the headset jack can greatly improve the audio quality.
Confirmed working on Xperia P, all versions of the app.
Also confirmed working on:
Don't forget to thank the original developer for his work