So I've upgraded VM to 3.0.16 and using PHP 7 still had the same problem.
With Joomla Error Reporting set to Development, I have noticed this message on the Media Edit page:
"
Warning: is_writable(): open_basedir restriction in effect. File(/tmp) is not within the allowed path(s): (/home/xxxxxxx/public_html) in /home/xxxxxxx/public_html/administrator/components/com_virtuemart/helpers/mediahandler.php on line 375"
and this at the bottom of the page:
/tmp :: Unwriteable
/home/xxxxxx/public_html/images/stories/virtuemart/typeless/ :: Unwriteable
/home/xxxxxx/public_html/images/stories/virtuemart/typeless/resized/ :: Unwriteable 
I then noticed that my PHP 7 Settings has open_basedir set to /home/xxxxxxx/public_html and no value for PHP 5.6.
This was restricting VM access to /tmp which I assume VM uses as a temporary upload destination.
I was thinking that /tmp was relative to the website root, i.e. public_html/tmp
So, no problem with VM and PHP 7 in this case

Thanks for your help.