Thanks both for your suggestions. No luck yet.
I have now included the following in each vhost's config section.
AddHandler php5-script .php
AddType text/html .php
Yes, my php files have .php extensions and I am using full '<?php' tags.
Unfortunately I didn't note down exactly what I did to get php back up, but I think it was mainly adding the php LoadModule line to /etc/httpd/conf/httpd.conf
LoadModule php5_module /usr/lib64/httpd/modules/libphp5.so
[I think the Plesk upgrade also overwrote httpd.conf]
Note this line already existed, unchanged, in /etc/httpd/conf.d/php.conf.
LoadModule php5_module modules/libphp5.so
Can I then deduce that php.conf is not being read/used because it didn't load the php module --- as it needed to be added to httpd.conf??
I just tried temporarily removing open_basedir in php.ini but no change.
I hope I am making sense.