Prof Hawking also said the popularity of Trump, who is now the Republicans' likely nominee for president, was beyond even his understanding.
The world-famous theoretical physicist has made no secret of his disdain for the preposterous billionaire, previously joking about his intelligence.
Asked if his knowledge of the universe meant he could explain the popular appeal of the billionaire tycoon, he told ITV's Good Morning Britain: "I can't. He is a demagogue, who seems to appeal to the lowest common denominator."
Prof Hawking also told the ITV show that Britain needed to stay in the European Union to protect its scientific research being undermined by the Government's austerity cuts.
He said Britain needed to stay in the European Union to protect its scientific research being undermined by the Government's austerity cuts, adding the UK would become "culturally isolated and insular" if Brexit limited the scope for foreign exchanges.
"There are two obvious reasons why we should stay in," Professor Hawking said of the science case - which he said came on top of arguments staying in was better for security and the wider economy.
"The first is that it promotes the mobility of people. Students can come here from EU countries to study, and our students can go to other EU universities," he said on Good Morning Britain.
"More importantly, at the level of research, the exchange of people enables skills to transfer more quickly, and brings new people with different ideas, derived from their different backgrounds. Without this exchange, we would become more culturally isolated and insular, and ultimately more remote from where progress is being made.
"The other reason is financial. The European Research Council has given large grants to UK institutions, either to foster research, or to promote exchanges.
"These grants are in addition to those given by the traditional UK research councils, which seem to be becoming progressively starved of resources, by a government intent on short-term cuts, without attention to the longer term consequences."
He went on: "Gone are the days we could stand on our own, against the world. We need to be part of a larger group of nations, both for our security, and our trade.
"The possibility of our leaving the EU has already led to a sharp fall in the pound, because the markets judge that it will damage our economy."
Vote Leave chief executive Matthew Elliott accused Prof Hawking of making a "patently ridiculous" argument for staying in the EU.
"The EU has been bad for science - increasing costs and bureaucracy," he said.
"The Clinical Trials Directive, for example, acted to double the cost of cancer research - as leading scientists and medical practitioners have acknowledged.
"In the internet age it is patently ridiculous to suggest that the referendum will have an impact on the exchange of information between scientists. And with our world-class universities, the calibre of scientists wanting to study here is unlikely to do anything except grow."