anotherthing,
At that time of night Thames Radar is not manned and Heathrow are usually 'resting their eyes'.
Up until 0300hrs rather than resting their eyes, whilst there will be no inbounds, LHR will likely have at least one if not two copper choppers on frequency to keep them awake.
So they are sat by the radar and keeping an occasional beady eye on it therefore any C130s or anything else flogging about at low level is likely to be noted.
Dizzee, if you're recording the H23 then why not look at your own recordings to see what's been happening, or do you switch the tape off at night?