Lord Peter Mandelson has urged Labour voters in the region not to be tempted to use the knife-edge referendum as a way of damaging David Cameron.
The Prime Minister has repeatedly insisted he will stay in Downing Street to carry out the will of the British people even if they ignore his pleas for a Remain vote.
However, it is seen as highly unlikely that Mr Cameron could survive in his post in the event of a Leave win.
Lord Mandelson, a key architect of Labour’s three general election victories in a row, said: “If Britain votes to leave the EU next Thursday it will be a Tory Brexit. You will have new, nastier, more right-wing Tories in charge who will strip away the rights people hold dear in this country.
“They will be targeting working people in northern areas of the country.
“Don’t take the risk.”
Lord Mandelson added: “If you get rid of Cameron you will still have the Tories but a nastier more right wing version.
“People need to realise the decision we take next Thursday isn’t a general election where we can change horses in a few years time.
“This will be irreversable for all time. once we are out and that is too big a chance to take.”
Lord Mandelson was speaking during a visit to the BASF chemicals plant in Bradford as Labour figures continued this week’s renewed effort to win over the party’s supporters who are now seen as crucial to both sides chances of victory.
Former prime minister Gordon Brown will strike a similar tone today as he joins council leaders from major cities across the country to make the case for Remain.
Leeds City Council leader Judith Blake and Sheffield City Council leader Julie Dore are among the signatories to a letter saying “If our cities are to continue to grow and prosper, we must remain a member of the European Union”.
Mr Brown will say the in the 1980s the Conservatives “turned our industrial heartlands into industrial wastelands”.
He will claim money from the EU “stood between our communities and further devastation” and those funds are now threatened by “Tory Brexiteers”.
Vote Leave has already promised the Government would ensure Yorkshire still received the £600m it has been promised in the latest EU funding round if the UK leaves.
Vote Leave chief executive Matthew Elliott said: “These are desperate times for the IN campaign - recycling a declaration of support that was first made in February and then repeated again in April.
“The truth is that the UK’s cities have prospered in spite of our EU membership, not because of it.
“Every week we send £350 million to the EU, enough to build a fully staffed NHS hospital. Our cities would benefit hugely if took back control of this money and spent it on our priorities - such as public services and infrastructure - instead. The only way to do this is to Vote Leave on 23 June.”
Vote Leave will try to put concerns over Turkey’s possible entry into the EU back at the centre of the referendum debate with a letter to David Cameron signed by fellow Conservatives Boris Johnson and Michael Gove along with Labour MP Gisela Stuart.
The letter challenges the Prime Minister to make clear the Government will veto Turkey joining the EU and will stop the extension of visa-free travel to Turkish citizens before next week’s referendum vote.