Blair acknowledged that both of the country's main political entities - the Conservative Party and the Labour Party - remained wedded to pulling Britain out of the European Union's single market.
In a separate interview with Sky News' Sophy Ridge programme, Mr Blair paid tribute to the veteran left-winger's temperament during the election campaign and how he mobilised younger voters.
Blair acknowledges - and laments - that his beloved Labour Party did not campaign against the Brexit.
Earlier, Mr Blair had suggested the European Union might be prepared to offer concessions over freedom of movement if Britain remained a member.
Brexit hardliners in the Cabinet and on the Tory backbenches are furious with Mr Hammond for championing a two-year transition deal to cushion the impact of leaving the EU.
BBC host Nick Robinson slapped down the staunch Remainer, who vowed to return to politics to thwart Brexit, over his proposed negotiations with the bloc's leaders.
Working groups will focus on three areas: citizens' rights; the EU demand that Britain pays some 60 billion euros ($70 billion) to cover ongoing EU budget commitments; and other loose ends, such as what happens to British goods in EU shops on Brexit Day.
In the BBC Radio 4 interview, he went on to suggest that Brexit - if followed by a government led by the current Labor party leader Jeremy Corbyn - would leave the United Kingdom "in a very serious situation".
That forecast bluntly contradicted a prediction by the International Trade Secretary Liam Fox who said last Thursday he would be "very happy" with a transition period of just "a few months".
The former Labour PM said Leave voters in the North were wrong to vote Brexit because it will make them poorer and claimed they lacked the right information during the referendum campaign a year ago. "I'm not going to disclose conversations I've had within Europe, but I'm not saying this literally on the basis of a whim".
Mocking the former PM over his failed ambition to become EU President, Mr Duncan Smith added: "I'm so sorry now that he can't find himself the president of Europe job which is what he wanted but the people of Barnsley and Boston aren't the slightest bit bothered about what he's thinking about".
John McDonnell has accused Tony Blair of being out of touch with the "nature of the debate" when it comes to Brexit negotiations.
Macron's victory "changes the political dynamics of Europe".
Speaking to BBC's Today programme, Mr Blair refused to name his sources in the European Union who had suggested officials may be willing to change free movement control to appease Britain. I haven't discussed my concerns with many people - and certainly not with any MPs from other parties.