As Deputy Prime Minister Nick Clegg and UK Independence Party leader Nigel Farage prepared to take to the airwaves to do battle over the future of Britain's membership, Sir Richard said that the UK should be "desperate" to remain a leading part of the EU.
Quitting the 28-nation bloc would be "a very grave error" and would do "enormous damage" to Britain's businesses, wrote Sir Richard - a prominent supporter of continued UK membership.
Writing on the Virgin website, he said: "Great Britain can't be allowed to become Little Britain. As part of Europe, people can live where they want, set up companies where they want, trade where they want, travel where they want. As part of the EU, there are many more countries for British people to experience, and vice-versa, making for a much more diverse, multicultural, rich society.
"For those people who seem hell-bent on pulling the UK out of the EU, it is contrasting that the people of Ukraine were willing to die on the streets of Kiev in hope that they could join the EU.
"There are countries all around Europe that are desperate to be a part of this great marketplace, and Britain should be desperate to remain a leading part of it."
Sir Richard said that "the last thing" the Government should do is make the lives of job-creating entrepreneurs more difficult by cutting ties with the EU.
"Fewer companies would set up business in the UK if they could only trade with 60 million people, rather than 500 million," he said.
"The EU is the UK's biggest trading partner. As the EU forges new partnerships with emerging markets of Latin America and Asia - plus extends existing relationships with the US and Canada - the UK must be at the centre to help. If the UK shuts the door on the EU, the door will be firmly shut in return and it would be very difficult to get back into the EU once we had left."
He predicted: "If the United Kingdom ever decided to leave the European Union, people would wake up and realise they had made a very grave error indeed."
Matthew Elliott, chief executive of the Business for Britain campaign for a renegotiated deal with the EU, said: "Richard Branson told Britain at the turn of the century that we'd be much worse off if we didn't join the euro. Now he is advocating Britain staying in the EU at all costs.
"The sensible option is not to defend the status quo or to leave tomorrow, but to push for real and substantial changes that will benefit all British businesses.
"The majority of UK entrepreneurs are totally in support of getting a better deal from the EU. That deal would include less regulation and a greater focus on trade and free trade deals, including with the likes of China, Russia and India with whom the EU is currently dragging its feet.
"No businesses want to lose access to the EU's 500 million consumers, but the vast majority also want to see real changes made to the terms of Britain's membership that will help them to grow and create more jobs."