OK, found it, for fellow 123-reg users:
There is a cpanel page that let’s you change your php version, but it’s limited to 5.2-5.5 and actually doesn’t necessarily reflect what’s going on!
The answer is the reverse of the start of this guide: https://www.123-reg.co.uk/support/answers/how-to-switch-the-php-version-4235/
Edit your .htaccess file and comment out (add a # before) the line
# SetEnv DEFAULT_PHP_VERSION 7
This will now allow the cpanel’s changes to have an affect.