The controversial member of the House of Lords has previously said her failure to register support from the not-for-profit company Equal and Free Limited - which was used to pay for her parliamentary researcher - was an "oversight".

The crossbench peer also failed to declare that she was an unpaid director of the company, which describes itself on its website as a "UK-based network of academics, parliamentarians, lawyers and women's groups" who "champion the rights of British Muslim women who do not (yet) have the protection of legal marriage."

In her letter to the commissioner, Baroness Cox offered her "profound apologies" over her failure to declare the interests.

She said she "never personally received funds from Equal and Free Ltd" but acknowledged since 2014 she had benefited from the support of part-time researchers employed by the company.

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Baroness Cox suggested to the commissioner that her frequent travel abroad for humanitarian work and limited staff support was behind her failure to register the interests in question.

"I can only offer an explanation of my failure with reference to the massive commitment to my humanitarian aid and advocacy work with the small charitable organisation I founded.

"This travel takes up much of my time and my colleagues and I return inevitably stressed by the suffering we witness and the obligation to report the situations (including in the House of Lords).

"I believe this goes some way to explain my failure to fulfil my responsibility to register and declare my directorship of and the research support I received from Equal and Free Ltd, for which I renew my apologies."

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But in his findings, the House of Lords' standards commissioner Martin Jelley said he did not "consider the reasons she provided for not registering and declaring her interests in Equal and Free Ltd to be sufficient".

However, he accepted that she did not receive "any direct financial benefit" from the company, and suggested she take remedial action for the breach by issuing a statement of personal apology to the house, which she has agreed to.

He said Baroness Cox's failure to declare her directorship and the support she received was in breach of paragraphs 12 and 15 of the code of conduct.

Paragraph 12 requires members to register all relevant interests that "might reasonably be thought to influence their parliamentary actions" while paragraph 15 says it is the responsibility of members to ensure that such interests are accurate and up-to-date, with any changes added within a month.

Mr Jelley said her failure to declare her interest in the firm "when participating in relevant proceedings" also made her in breach of paragraph 17, which requires members to fully declare their interests.

As part of its Westminster Accounts project, Sky News obtained minutes of meetings which reveal that Equal and Free Limited has received funding from an American organisation run by two evangelical philanthropists.

Based in Los Angeles, Fieldstead and Company handles the donations of Howard Ahmanson Jr and his wife Roberta Ahmanson, and focuses support on "religious liberty issues" as well as art, culture and humanitarian relief work.

In a 2011 interview with Christianity Today, Mrs Ahmanson said: "We are probably the single largest supporter of the intelligent design movement, and have been since the beginning."

Intelligent design argues that aspects of life are best explained by the involvement of a higher being rather than evolution.

The couple has also been linked to orthodox Christian groups and political campaigns against same-sex marriage.

There is no suggestion of any wrongdoing against Fieldstead and Company.

While parliamentary rules require peers to disclose support received from outside organisations, they are not required to detail where funding originated initially.

Baroness Cox was forced to declare the financial interests following the huge leak of documents revealed by Sky News.

In her response to the commissioner, she said Equal and Free Limited "was only ever established to support my own interests - shared by many others - in the plight of Muslim women".

The standards commissioner opened his investigation after receiving a complaint from Liron Woodcock-Velleman, the former political organiser of Hope not Hate, in February.

Sky News has approached Baroness Cox for comment.