John McDonnell has criticised Theresa May’s rumoured approach to persuading Labour MPs to vote for her Brexit deal as “pork-barrel” politics, saying: “If there is money there to spend on our constituencies, it should be done anyway.”

The shadow chancellor’s accusation follows reports that the government is preparing to plough extra funding into deprived areas that supported leave, with the Nottinghamshire MP John Mann claiming that a set of job-creation measures targeted at former industrial towns would make it “very difficult for Labour MPs in leave areas to vote against the deal unless they want a second referendum”.

However, the Redcar MP Anna Turley dismissed the offer of “bribes or sweeteners … which we know will make those constituencies worse off”.

McDonnell said on a visit to Stoke-on-Trent on Saturday: “The Conservatives introduced pork-barrel politics straight after the general election because they gave a couple of billion [pounds] to the DUP just to secure their votes,” said McDonnell, the shadow chancellor.

“It was something like £100m a vote they spent to get the DUP supporting them, so they already introduced that pork-barrel contractual politics. I think it degrades our political system and to try and extend it in this way, I think it’s dangerous for our democracy.

“So what most MPs have said is, actually if there is money there to spend on our constituencies, it should be done anyway. It shouldn’t be done in return for votes.”

Questioned on whether Labour rebels would be punished following Tuesday’s key vote, McDonnell said it was a matter for the Labour chief whip. “We introduced a whip, we expect people to abide by it, but there’s an understanding that in some areas, you can understand why some people voted the way they did.”

McDonnell said conversations about “contractual” arrangements pledging investment in the constituencies of MPs who back the prime minister’s deal, first reported in the Times, was “dangerous for our democracy” and would amount to MPs selling their votes. “I don’t think any MP will sell their votes in that way – that sort of bribery and corruption,” he said.

A spokesman for the prime minister this week confirmed ministers were looking at a programme of “national renewal” following Brexit to tackle inequality and rebuild communities, but said he “absolutely wouldn’t characterise” the reported investment offer as “cash for votes”.

“We are determined to lead a programme of national renewal post-Brexit by rebuilding and reconnecting communities, driving prosperity and unleashing the potential and creativity of hard-working people in every part of our country,” the spokesman said.

In an article on Saturday in the Daily Mail, the Labour MP John Mann said he would not apologise for trying to get a better deal for his constituency, admitting that some MPs were seeking to leverage the government’s need for support on Brexit to their advantage.

“If [Theresa May] gives a cast-iron commitment to a national rebuilding programme that’s truly transformative in scale, and will help communities woefully neglected for decades, I will be delighted,” he wrote.

“Will that make it easier for more Labour MPs to vote for her Brexit deal? Yes. But that is not bribery, it’s politics.”