Bournemouth MP Conor Burns had used Commons stationery in February last year to write to a person representing a company involved in a dispute with his father over the repayment of a loan.
An ally of British Prime Minister Boris Johnson resigned his ministerial post on Monday after an inquiry found he used his position to try to intimidate someone involved in a family dispute.
Conor Burns quit as junior international trade minister after a House of Commons standards committee recommended he be suspended from the lower parliamentary chamber for seven days.
Burns had used Commons stationery in February last year to write to a person representing a company involved in a dispute with his father over the repayment of a loan.
The MP for Bournemouth, a town on the southern English coast, suggested he could raise the case in parliament, where anything he said would be immune to any legal proceedings.
"Mr Burns used his parliamentary position in an attempt to intimidate a member of the public into doing as Mr Burns wished, in a dispute relating to purely private family interests," the committee's report states.
The commissioner for standards, Kathryn Stone, who carried out the inquiry, said his behaviour had a wider impact than simply breaching the MPs' code of conduct.
It "gives fuel to the belief that members are able and willing to use the privileges accorded them by their membership of the House to benefit their own personal interests," she said.
Burns was an aide to Johnson when he was foreign secretary and is also a committed supporter of Britain's decision to leave the European Union.
"With deep regret I have decided to resign as minister of state for international trade," he tweeted, saying that the premier continued to have his "wholehearted support".