I had this problem myself, and a big argument with BMW since the instruction book with my Mk3 seemed to be telling me that TMC should work. Here's an extract from an email from BMW customer service:
"
From production September 2003, all cars fitted with navigation systems benefited from the introduction of a DVD disc based system and the introduction of TMC. To reflect this change, all navigation options increased in price at this time in order for customer to pay for this new technology. We can confirm that you purchased your vehicle before these changes took place and did not purchase the navigation system which included TMC.

If you would like this function on your vehicle, it may be possible for you to enable the TMC at your local BMW Dealership. We would advise you to speak to the Parts Department situated within your local dealership who will be able to submit a Technical enquiry which will determine if it is possible to activate this function on your specific vehicle or not. If this upgrade is possible, they will then be able to inform you of the costs of retro fitting this function.

If you require the contact details of your local BMW Dealership, you are able to locate this information on our website www.bmw.co.uk.

We are sorry that this may not be the answer that you may have anticipated and hope this clarifies why TMC is stated in the handbook and on your vehicle but is currently unavailable for you to use.

Your reply from BMW is correct, they did not include the required codes on the CD map disks, only the DVD map disks. However, they this is not the only way to enable TMC on the BMW nav system.

In Europe you will find that TMC works even with the BMW CD maps, this is beacuse TMC is run as a free service and does not require codes on the map disk. In the UK the service is run by a company called ITIS, they get their income by charging more for a map disk that has the required TMC codes.

The BMW system is basically a badged VDO Dayton system, you can use the VDO Dayton map CD's in a MK III (I did when I had mine). If you go to the VDO Dayton shop http://www.vdodayton-shop.com/start....=18&ShowLand=1 (for some reason this page always comes up in German, even though the link is from the English version of the page! If you want it in English then start from the www.vdodayton-shop.com page and navigate through to the UK map disks) you will see that there are two versions of the UK/Ireland map CD, one with and one without ITIS TMS codes.

I found another fix - buy a later model with Mk4 DVD nav!

That would do it! Or buy a MK IV Nav computer, they are externally identical and have the same connections.