The tycoon claimed it was "important that people have a second chance" if "the facts change or once the facts are known", following negotiations to leave the EU.
He told the Press Association: "The people voted for the Government to come out of Europe based on Â£350 million more going into the NHS, and a whole lot of things they were promised.
"Let's see if these promises come true in a year or two years' time - and if those promises are not on the table and in fact the country is really suffering, and the costs are going to really cripple the country, then it's important, I think, there are MPs who can stand up and say something needs to be done about this - we can't just destroy a beautiful country."
Sir Richard, who was speaking at the inaugural Virgin Sport Hackney Festival of Fitness in east London, said that he was not "wanting to change the will of the people" despite his company giving thousands of pounds to the organisation behind a campaign to encourage people to vote tactically in the General Election.
The billionaire said he helped to "pay for the office" which is used by Gina Miller, the businesswoman whose legal action forced a parliamentary vote on withdrawal from the EU.
She launched the Best For Britain crowdfunded initiative to influence the result in marginal seats last week.
Sir Richard's Virgin Management Limited put Â£25,000 towards the start-up costs of UK-EU Open Policy Limited in January, which runs the Best for Britain campaign.
He explained: "If the negotiations mean that Britain is going to be damaged, we want to be sure that this office looks at the negotiations carefully and doesn't just let the Government get away with pushing through an outcome that is really bad for Great Britain.
"I put a bit of money into helping fund the office and then I think since then Gina Miller is using that office as well."
The Virgin boss said that people had voted in last year's referendum without knowing the "truth", and said that "when everything has been negotiated, the House of Commons really should be given the facts and they should vote on whether it's a good idea or not".
"A hard Brexit would be, I think, a disaster for this country and therefore if they try to push that through, it's not what people were promised and it's important that people have a chance to have another think."
However, Sir Richard added: "If they can negotiate something which is in the interests of Great Britain that's great, let's go with it.
"But if it's palpably not in the interests and the country is being damaged then MPs should decide on these things, and have a say, in my opinion."