Sorry, the information I gave you was slightly wrong.
3.6.4 was working fine with WP 3.0.
2 days ago I logged on to my web host and received a message to upgrade WP to 3.1 (I did this by responding to the webhost message - not within WP).
After this I logged on to the WP dashboard and realized that 3.1 had already been superseded by 3.1.1.
I upgraded again, this time automatically through WP.
I appreciate that the above actions were stupid, because I did not test my site after the first upgrade (WP 3.0 to 3.1) so I'm not sure if 3.1 or 3.1.1 has caused my blank screen problem.
Also another thought. Is it possible that if my webhost has changed something, it would only show up on later versions of WP ie 3.1 onwards?