I just go Moodle 3.1 running under Ubuntu 16.04 using a slight variation of the step-by-step instructions for 14.04
Here is a mapping of the pacakge changes:
php5 --> php7.0
libapache2-mod-php5 --> libapache2-mod-php7.0
php5-pspell --> php7.0-pspell
php5-curl --> php7.0-curl
php5-gd --> php7.0-gd
php5-intl --> php7.0-intl
php5-mysql --> php7.0-mysql
php5-xmlrpc --> php7.0-xmlrpc
php5-ldap --> php7.0-ldap
You will also need:
php7.0-xml (a fatal error during Moodle setup occurs unless this has been installed)
php7.0-zip
If you need to change php parameters, file /etc/php5/apache2/php.ini has moved to /etc/php/7.0/apache2/php.ini
Best Regards,
Bob Thomas