David Cameron has ordered an inquiry into whether Conservative Party co-chairman Baroness Warsi breached the ministerial code when she was accompanied by a business partner on an official visit to Pakistan.

The Prime Minister called in Sir Alex Allan, his independent adviser on ministerial interests, to investigate after she admitted failing to disclose her business relationship with Abid Hussain.

Lady Warsi wrote a letter of apology to Mr Cameron, saying she was "sincerely sorry" for the embarrassment to the Government.

The Cabinet minister is facing mounting difficulties, with the prospect of a sleaze inquiry into separate allegations about her House of Lords expenses claims, into which Labour are demanding a criminal investigation.

Mr Cameron's referral of her relationship with Mr Hussain to his adviser on the ministerial code comes despite his steadfast refusal to order a similar inquiry into Culture Secretary Jeremy Hunt, who has faced weeks of heavy criticism for his contacts with News Corporation over its attempts to take full control of BSkyB.

Labour said the Prime Minister's actions underlined that he was "bending over backwards" to defend Mr Hunt.

Mr Hussain attended Lady Warsi's July 2010 visit to Pakistan - soon after she had joined the coalition Cabinet. They were both directors of a company called Rupert's Recipes.

In her letter to the Prime Minister, she said "community activist" Mr Hussain was among a number of members of the Pakistani diaspora in the UK who had assisted the British High Commission with outreach events in Pakistan in July 2010.

Although it was "widely known" that he was her husband's second cousin, she said, she had not realised the need to declare that they also had "a common business interest as minority shareholders in a small food company".

"I sincerely regret that I did not consider the significance of this relationship with Mr Hussain when the arrangements for the visit were being made. In retrospect, I accept that I should have made officials aware of the business relationship between Mr Hussain and myself, and for this I am sorry," she wrote.

"I regret that this failure may have caused embarrassment to the Government."

Lady Warsi stressed that it was not a trade-related visit and Mr Hussain "did not gain any financial or business advantage" from his involvement, he was not part of the official delegation and no aspect of his visit was funded by the Government.

"As a final point, the visit of July 2010 was organised within a few weeks of my appointment. It was at a time when my office accommodation and staffing were still being settled and I was finding my feet within Government. However, I have at all times disclosed my own personal financial interests in full on the register of Ministerial interests," she wrote.

"On a personal note, David, I am sincerely sorry for these difficulties."

The Prime Minister said he accepted her apology but was asking Sir Alex to "consider the issues that have been raised with respect to the Ministerial Code and to provide advice to me as rapidly as possible".

Mr Cameron responded that she should have "proactively" raised the business interest she shared with Mr Hussain with the Foreign Office and the Cabinet Office.

He wrote: "The Ministerial Code requires ministers to ensure no real or perceived conflict between their official responsibilities and their personal interests.

"However, as you say, you did declare to the Cabinet Office your own interest in the company, and I note too the other points you make - in particular that this was not a trade-related visit, and Mr Hussain did not gain any financial or business advantage from his involvement in voluntarily assisting the High Commission with the event.

"This seems to me to be important to take into account in responding to this issue. I accept too your apology for your error and for any embarrassment to the Government.

"There are clearly some lessons for future handling and I have asked Alex Allan, my adviser on Ministers' interests, to consider the issues that have been raised with respect to the Ministerial Code and to provide advice to me as rapidly as possible."

Shadow Cabinet Office minister Michael Dugher said: "It is right that David Cameron has finally called in the independent adviser on the Ministerial Code after a week of pressure from Labour and the media, as Baroness Warsi clearly has very serious questions to answer.

"Did she break rules that peers should declare their business interests, particularly if they are the principal shareholders in a company? Why was it considered acceptable for a foreign government to pay for her visits to the Middle East? Did Baroness Warsi claim for expenses that she did not, in fact, incur?

"But David Cameron's actions in this case draw into sharp relief his refusal to hold a similar investigation into Jeremy Hunt, despite clear evidence that he broke the Ministerial Code by misleading the House of Commons on at least three occasions.

"David Cameron is bending over backwards to defend Jeremy Hunt because he knows that it is his own judgment, in appointing a man he knew to be biased to oversee the BSkyB bid, that is in question."