Its well known that the LE500 has problems with its reverse sensors usually sounding continuously when its wet, once reverse gear is selected.
MG have replacements but apparently these are on back order and have been for some time, in addition when replacements are fitted, they need to be painted to match the bumper.
On my car, the reverse sensors would only play up occasionally but still annoying when it happened. I know I could have had the problem sorted under warranty but my nearest dealer is quite distant and after chatting with them previously about getting touch up paint and how difficult the vibrant orange is to match, I was not confident they could paint new sensors that would match.
Instead I decided to have a go at fixing them myself and after testing for the last 3 months, it has worked.
First the rear bumper needs to be removed, this has been covered many times before so I have not detailed this method again, follow CJJ's guide here
http://forums.mg-rover.org/showthread.php?t=288282
The only extra thing to do is locate the large multi-plug that powers the reverse sensors and unplug before the bumper is lifted away.
Next place the bumper on a soft surface and locate the components – the black circles show the 3 reverse sensors, the red circles show the 2 number plate light connector plugs
Give the various plugs and sensors a clean then seal the ends of the plugs to prevent water and moisture getting in. I used Arldite but would expect silicon sealant to do the same job.
The rear of the sensors also require to be sealed
Allow the Arldite to set then seal the plug connectors with insulating tape
Then re-fit the bumper.