Issues since upgrading server from php 5.4 to 5.6

A number of websites with open cart are having issues since upgrading from php 5.4 to 5.6, we are getting the below error:

Deprecated: mysql_connect(): The mysql extension is deprecated and will be removed in the future: use mysqli or PDO...

I can see there was a thread on this previously : http://forum.opencart.com/viewtopic.php?f=20&t=163163 however no fix was given at that time. Does anyone have a quick run down on what will need to be done to update the install to run using 5.6 or is there an article I would be able to reference? I will be unable to give FTP logins to these accounts

Any help would be very much appreciate

Like the error message says, MySql database is deprecated. MySqli or PDO are the answer.

Basically it looks like you need to backup all your data, do a clean install using MySqli (or PDO) and re-inject your data in your tables. There is obviously a risk of losing data ...

Perhaps it is also interesting to know exactly why it shows up. The entire ext/mysql PHP extension, which provides all functions named with the prefix mysql_, was officially deprecated in PHP v5.5.0 and removed in PHP v7.