OK - panic over (almost) it was a simple fix after all - I changed the TimeZone in config.php and it moved everything to where it should be (however, in Asia/Riyadh we don't have DST so I'll have to manually change it to +3 from +4 when the clocks change???)
MyCalendar and ScheduleCalendar works fine - but roscalendar.php is blank

I can't find how to fix this now. It's not really a big deal since it's read-only and the users have to log in to place a reservation, but it's a nice feature to have.
I found this:
<?php
date_default_timezone_set('Asia/Riyadh');
$script_tz = date_default_timezone_get();
if (strcmp($script_tz, ini_get('date.timezone'))){
echo 'Script timezone differs from ini-set timezone.';
} else {
echo 'Script timezone and ini-set timezone match.';
}
?>
and think it might help, but can't find my php.ini and if I did, I am not sure where to put the script. Any ideas? I am a secretary, who noodles around, not a programmer :-)
Cheers, Ellie