Your comments helped resolve the issue!

All I had to do was to change the exec line from:

exec "nohup ./error_summariser.cgi $identifier > $default_files_dir/$i
+dentifier/processing-log.txt &" or die "Can't exec: $!\n";
[download]

to:

exec "nohup ./error_summariser.cgi $identifier > $default_files_dir/$i
+dentifier/processing-log.txt 2>/dev/null &" or die "Can't exec: $!\n"
+;
[download]

Adding the sending of standard error to the null device now lets the webpage complete immediately.

Thanks for your help.

Paul McIlfatrick