Under an Oxford County Court ruling, made last week, Mr McEwan was given permanent custody of the children, who were due to be handed over before midnight on Monday. Ms Allen said she hoped her actions would prompt the Home Secretary, Jack Straw, to launch an inquiry into the case.
Earlier this year Ms Allen wrote to the Lord Chancellor in an attempt to overturn a judgment that gave the author temporary custody of the children. The Lord Chancellor has declined to intervene.
In a written statement released on Sunday, Ms Allen said: "I have pursued every channel in order to protect my children, and now as a last resort have written to the Home Secretary."
She added: "I shall not be returning the children to Mr McEwan as required by the court and am asking for a full inquiry into the case." Her boyfriend, Ismay Tremain, speaking from Brittany, said that Ms Allen and the boys were in a secret location in the province and were waiting for Mr McEwan to make the next move. Mr Tremain said he did not think it would be long before "the gendarmes" arrived.
Mr McEwan, who first rose to prominence as a short story writer, went on to win the Booker Prize with his 1998 novel Amsterdam. He is understood to have been in Switzerland on holiday and had agreed to let the children spend time with their mother. Mr McEwan divides his time between Oxford and London, where his present wife has a home.
Ms Allen and Mr McEwan were married in 1982. The custody dispute has continued since the marriage was dissolved in 1995. Mr McEwan married Annalena McAfee, a journalist, in 1997.
In her statement, Ms Allen said she "did not want to take the law into her own hands", nor did she want to "prolong the uncertainty" for her children. But, she added, as a "responsible parent" she had no choice.
Mr Tremain said Ms Allen had had a "really rough deal", which resulted last week in her being awarded maintenance of pounds 5,000 a year. He claimed she had spent nearly a million pounds on legal fees and other expenses in the long-running litigation: Ms Allen estimated Mr McEwan's annual earnings at between pounds 300,000 and pounds 500,000.
Ms Allen, who lived in rented property in Oxford, near her children's schools, claimed there had been irregularities in the case. Mr Tremain said that Ms Allen, who represented herself in the court hearing for financial reasons, found that previous court restrictions had made her life difficult.