Installation problem solved
Today I have added an alternative and newer version of PHP 5.5 to my server and immediately I find I can install BackdropCMS.
My VPS, using Plesk 12.0.18, had been provided with PHP 5.5.9 and this has proved satisfactory for several Drupal 7 sites, so it was a setback to be unable to install Backdrop yesterday.
I had no idea how to track the problem - I could find no error reports within my server logs, but this may well be lack of knowledge on my part.