I followed the advice and I have managed to deactivate the plugin by renaming the folder. I'm relieved to say that I can now login and see everything again! :) I also displayed the plugin page and noted that it displayed this message at the top of the screen:
"The plugin backupwordpress/backupwordpress.php has been deactivated due to an error: Plugin file does not exist"
I edited the wp-config.php file and changed WP_DEBUG to true
I also added the following additional parameters in wp-config
* Additional debugging information added by David Rose 12/08/2013
* Comment out them after testing has completed.
define( 'WP_DEBUG_DISPLAY', false ); // Hides the errors.
define( 'WP_DEBUG_LOG', true ); // Logs errors to wp-content/error.log
* End of additional parameters added by David Rose 12/08/2013
After logging out, I then went to wp-content to look for an error.log file but there wasn't one present. Having said that, apart from the missing plugin, no errors have yet occurred.
Now, referring back to your reply, you suggest that I send a screenshot of the Backups page, but I think I need further information on what to do now.
Should I rename the plugin folder from "Temp_backupwordpress" to "backupwordpress"?
In order to then produce an errorlog file, should I then reactivate it?
I'm happy to try and work through this and see if I can get backupwordpress working, because it looks like it will satisfy my requirements. However, I am cautious because I should really be dedicating my time to considering the content of my new blog...
Anyway thanks again for your advice so far.