Just bought BMW M5, May 05, Registered. It has a full BMW service history, only done 41,000 miles.
I was extremely unhappy when I was driving home from picking the car up, when I noticed a serious fault with the car (Which I also noticed with my previous car, a Jaguar S Type R, 54 plate) when accelerating and easing off the throttle I can hear a loud knock or clunk.

Could it be excessive play in the running gear? Or possibly: bushes, gear box, prop shaft or half shaft problems?
Or is this a manufacturing fault on early models?
Thanks for your reply.

I did take the car for a 10 mile test drive, however I did not notice the problem during the test drive, I only noticed it when driving back home after the purchase. I am ringing the main dealer tomorrow to see what they suggest.

Bring your car to a dealer for diagnosis.
Or at least to a knowledgeable BMW technician. I am sure you do not even know where the noise is coming from. So how do you know that it is a serious defect?
AND why did you buy this car in the first place without even doing a roadtest or having it checked by a mechanic?
Blame yourself and not BMW.

its a dodgy game buying a high performance car like that ..the reason you buy one is to drive the legs off it ..without looking at it you can only give an educated Guess...it could be many things ..from drive shafts to diff ..might be engine mounts ..or gearbox mounts ..prop-shaft ..unlikely half-shafts ..but i suspect its in the suspension area ..rear axle mounts and sway bars ..torsion bars etc all those things that hold the rear axle in place check all connection to front suspension ..they take a hell of a pounding from strong acceleration ..could even be exhaust flexing under braking and acceleration