Can't get web authorisation working on PC

I’m having no success trying to get web authorization to work in place
of the RT login. I find that once I’ve passed the web auth dialog I
still get the RT login prompt. I have a site config with
Set($WebExternalAuth , 1);
and I’ve tried both undef and 1 for
Set($WebFallbackToInternalAuth , 1);
but the behaviour always seems to be the same - the RT login page comes
up.
I have verified that the value for REMOTE_USER is the same as a
registered RT User.
I know that the web auth works because I use the same set up for my SVN
repository.

Can anyone please suggest what I am getting wrong?

Neville