The leading Brexiter John Redwood has insisted that his knighthood in the New Year honours list will have “no bearing whatsoever” on his intention to vote against Theresa May’s EU withdrawal deal.

Supporters of a second EU referendum have accused the prime minister of trying to exploit the honours system to secure support for her Brexit deal ahead of a crucial Commons vote, expected in January.

Redwood dismissed the accusation as “an obvious untruth”, and said no suggestion had been made to him that he should change his stance in exchange for an honour.

Redwood was among three MPs awarded knighthoods, alongside the Conservative former minister Gary Streeter and Labour’s deputy chief whip, Alan Campbell.

A leading supporter of the Best for Britain campaign for a second referendum, the Liberal Democrat MP Layla Moran, said the announcement brought “dishonour” on the system. “I cannot see how it is anything but a desperate attempt to blunt criticism of the prime minister’s Brexit deal by dangling a knighthood or two in front of MPs,” she said.

“Knights of the realm are meant to represent the best of being British, not backstabbing Brexit extremists like John Redwood. It just shows how weak Theresa May is that she is seen to be rewarding him for his behaviour.”

The Lib Dem MP Layla Moran says Theresa May is using the honours system to try to rally support for her Brexit deal. Photograph: Greg Blatchford/Rex/Shutterstock

The Scottish National Party MP Brendan O’Hara said: “Theresa May’s blatant abuse of the honours system is clear, as she continues offering grubby inducements to MPs in an attempt to persuade them to vote for her faltering deal.”

However, Redwood told Sky News: “It has not bearing whatsoever on my view of the withdrawal agreement. Today, as before I was offered the honour, I think the withdrawal agreement is a very unwise choice for the UK and so, with regret, I can’t vote for it.”

He denounced the suggestion the award was an attempt to buy his support as “a lie”, adding: “I think it’s a pity to taint the public debate with such an obvious untruth. No one ever suggested that I should change my conduct in return for a knighthood and had they suggested that, I would have given them a very sharp reply and explained to them that is not the purpose of the honours system.”

Redwood published a blog days before the announcement of his honour titled “Eight things wrong with the Withdrawal Agreement”.

Streeter, who backed remain in the 2016 referendum, has already made clear he supports May’s deal.

Redwood was one of the Eurosceptic cabinet ministers branded “bastards” by John Major as he fought to ratify the Maastricht Treaty in 1993, and has continued to fly the anti-EU banner in the Commons ever since. He headed the 10 Downing Street policy unit under Margaret Thatcher from 1982-87, where he was a champion of privatisation.

Redwood has been the MP for Wokingham in Berkshire since 1987, and became Wales secretary in 1993, memorably struggling to sing along to the Welsh national anthem at his party’s annual conference in Wales.

His clash with Major over Europe came to a head in 1995 when the prime minister called on his critics to “put up or shut up” and resigned to trigger a leadership contest. Redwood stood against him, but received only 89 votes to Major’s 219. After being defeated in a second bid for the leadership in 1997, he returned to the Tory front benches from 1997-2005 under William Hague and Michael Howard.