Mr Blair, who left office in 2007 and has since made millions through consultancy work, speeches and book deals, weighed in on Brexit on Friday with a speech in central London.
BBC presenter Peter Allen criticised the former Prime Minister for his intervention, which saw Mr Blair call for an uprising against Brexit.
The broadcaster, who has been with BBC Radio 5 Live since the station started in 1994, criticised the 63-year-old as not helpful to the UK’s negotiations with the EU and suggested his views should be disregarded.
Speaking to Sky News' Adam Boulton on All Out Politics, he said: “We’ve got to be tough about this and we’ve got to stand actually together.
Peter Allen has labelled Tony Blair "irrelevant" on Brexit
What Tony Blair is saying is an irrelevance and a distraction
“I hate to say this, I’m not saying which way I voted, but we have to work from here on in and what Tony Blair is saying is an irrelevance and a distraction.”
Mr Blair attempted to mobilise fellow Remainers to fight against Brexit by telling them to “rise up in defence of what we believe”.
He suggested voters were lied to before they voted on the UK’s divorce from the EU.
It was the former Labour politician's first major speech since the EU referendum last June.
He said: “The people voted without knowledge of the true terms of Brexit. As these terms become clear, it is their right to change their mind.
“Our mission is to persuade them to do so."
Get Quotes on Home Insurance
Tony Blair has called for an uprising against Brexit
Blair and Juncker: Together through the years
Wed, January 25, 2017
Former Prime Minister, Tony Blair and President of the European Commission, Jean-Claude Juncker have always shared a friendly relationship over the years.
1 of 8
EU Commission President Juncker greets former British PM Blair in Brussels
He also urged pro-EU supporters to “expose relentlessly” the prime minister’s drive to push “Brexit at any cost”.
The Government is ahead of its March 7 deadline to push its European Union Notification of Withdrawal Bill through Parliament, after a successful vote earlier this month.