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The Opinium study for the Observer found the Tories on 37%, down three points on last week.
Labour is up one point on 36%, the Liberal Democrats up one on 9% and the Greens down one on 6%.
Mr Johnson’s net approval rating was -20, the lowest rating it has been with the pollster – down from -16 last week – with 30% of those surveyed approving of the job he is doing and 50% disapproving.
Sir Keir Starmer’s rating remains on -9, with 29% approving and 37% disapproving.
It comes as former prime minister Sir John Major launched an extraordinary broadside at the government over the row.
The Conservative former premier said the conduct was “shameful” and had trashed the reputation of Parliament.
And he suggested the Johnson administration was “politically corrupt” over its treatment of the House of Commons.
The Prime Minister was forced to U-turn over a plan to prevent Mr Paterson facing a 30-day Commons suspension for a serious breach of lobbying rules.
Mr Paterson subsequently quit as an MP after the Government abandoned an attempt to set up a Tory-dominated committee to re-examine his case and the wider Commons standards regime.
Sir John said: “I think the way the Government handled that was shameful, wrong and unworthy of this or indeed any government. It also had the effect of trashing the reputation of Parliament.”
The former prime minister, whose opposition to Brexit has seen him at odds with Mr Johnson’s Government, told BBC Radio 4’s Today the action of the current administration was “damaging at home and to our reputation overseas”.
Opinium surveyed 1,840 UK adults on November 5-6.