Well after weeks of following the Alexa rank of various websites, I've concluded that it a bit of a joke.
The rank is supposed to be site-based, but I'm now getting different ranks for different pages of the same site. What's more, some of the less popular pages have a higher rank than the others.
Other sites, where I monitor only one page, sometimes return a wildly different rank from two visits within minutes of each other.
I've tried re-installing the Alexa toolbar, which has appeared to fix strange anomalies before, but it made no difference whatsoever.
What makes it worse is that I am now experiencing the same effect when I view the rank from home and at work.
So, although I shall probably continue to monitor the rank (I have a system set up to do it automatically), I shall not be taking it very seriously until they fix this bug.