For the W98/W2K/XP environment I am looking for an executable/DLL
which will capture the HTTP stream going to and from a web browser. I
want the HTTP stream to be written to disk on the client.

I have found and used Sockspy (it's very good)...

http://sockspy.sourceforge.net/sockspy.html

...but I do not want to have to install TCL on the client. Also
SockSpy has quite a user interface whereas as far as possible what I'm
looking for should be invisible to the user.

Either the source code (VB/C++/Java/ASM) should be available (due to
it being share/freeware or an MSDN type giveaway) or the product
should have
very little user interface (ideally no more than an icon in the system
tray).

The solution should not be restricted to use with MS browsers/servers.

I accept that the client browser may have to change proxy settings in
order to allow this to operate - that's not a problem.

Just to flesh this out a little I should explain that I wish to write
an app (to run on the client) which would analyse the actions of the
user and make these available visually on the client. The data
captured from the HTTP stream would be the input to this app.
 
Let me know if I need to tell you more.

Analyzer is quite popular and is public-domain, source available:

http://analyzer.polito.it/

Check out the program's block diagram:

http://analyzer.polito.it/docs/advanced_man/images/general_structure.gif

You should be able to hard-wire the program to be GUI-less, port
80-specific, or even just use the program as sample code to libpcap.