Sorry to answer own question but in the hope it might help others.
Couldn't find a single threaded browser that ran on windows.
I read various web based comment on increasing max sessions for browsers on Windows. All involved changing or creating registry entries. [ While I wanted to reduce max sessions, as Sam offered (see answer below), it seemed logical that if max sessions was set to one I would get the single threadedness I required. ]
Exactly what registry changes were required depended on Windows version and Browser version.
Despite trying a wide range of changes with a wide range of browsers I did not ever have success reducing max sessions to one.
However with Windows 7 and IE 11 I could also see no relationship between the registry settings and the number of connections. At one point I had 12 connections open yet the biggest registry entry was 6.
Seems registry settings and behaviour have at best a very hazy relationship. Certainly not one that one could rely on.
We've decided for our purposes to preprocess network traces which is an extra step but c'est la vie.
Cheers all who viewed.