MPs and peers have refused to back the Government's preferred candidate to be the new chairman of the Equality and Human Rights Commission (EHRC).
The Joint Committee on Human Rights and the Women and Equalities Committee said concerns relating to "potential or perceived" conflicts of interest had to be addressed.
The committees said they were "unable to recommend that this appointment should proceed" because of David Isaac's links with a City law firm.
Both committees were involved in pre-appointment scrutiny of Mr Isaac, who intends to remain as an equity partner at Pinsent Masons, a firm which advertises its "extensive experience" working with Government.
In a letter to Education Secretary Nicky Morgan, who is also the Minister for Women and Equalities, the two committee chairwomen set out why they considered this to be an unsuitable arrangement.
Harriet Harman, chairwoman of the Human Rights Committee, and Maria Miller, who chairs the Women and Equalities Committee, said Mr Isaac would be a "good candidate" if the issues could be addressed.
The two former Cabinet ministers said they had received legal advice "which confirms our view that Mr Isaac's appointment, in conjunction with his continuance as a senior equity partner of a law firm which conducts a significant amount of business with the Government, would constitute a serious potential conflict of interest".
The appointment could also jeopardise the international "A" status given to the EHRC, they said.
Measures proposed to minimise the potential conflict of interest do not go far enough, the committee chairwomen concluded.
"We do not consider that these rise above the level of general assurances that Mr Isaac will remove himself from discussion or decision-taking in relation to an exercise of the Commission's statutory powers in relation to a client of Pinsent Masons.
"We also note that these proposals specifically exempt any such removal by Mr Isaac in cases where the Commission is exercising its powers on a sector-wide basis.
"We further note that they do not address the concern that Mr Isaac will have a continuing financial interest.
"We do not consider that these measures are sufficient to tackle the problems we have identified. We find it difficult to see how this matter might be resolved if Mr Isaac wishes to continue as an equity partner at Pinsent Masons while in the role of chair of the EHRC."
They continued: "We are not satisfied that the steps that have been set out for tackling this problem are sufficient to allay our concerns, and therefore we are unable to recommend that this appointment should proceed."
A Government spokesman said: "We are pleased the committees have recognised ?that David Isaac is a good candidate, as have other prominent figures from the human rights and legal community, including Lord Lester and Lucy Scott-Moncrieff.
"We will, of course, look at all issues raised by the committees, and expect to respond very soon."