The ad was run as part of ADI's My Mate's a Primate campaign against primates being use in circuses, films, TV programmes and advertising.
ADI had appealed against a ruling by the High Court last year that the ban on ads by groups deemed "political" under the 2003 Communications Act breached the freedom of expression provisions in human rights laws. ADI argued that the ban, aimed mainly at political parties, is too wide - a view shared by many other pressure groups who want to advertise on TV and radio.
But today's judgement said that in a democratic society, competing views and opinions must be given a level playing field.
It said that this would not be achieved if interest groups were able to buy airtime to give enhanced prominence to their views.
It said: "The risk is that objects which are essentially political may come to be accepted by the public not because they are shown in public debate to be right but because, by dint of constant repetition, the public has been conditioned to accept them."