Michael Gove faces accusations that he may have misled parliament over claims of bullying and intimidation by key advisers at the Department for Education.

The Observer can reveal that a senior civil servant in the education secretary's department has received a secret payoff of about £25,000 out of public funds, after a lengthy grievance procedure involving members of Gove's team, including his special adviser, Dominic Cummings, and the department's former head of communications, James Frayne.

While an investigation within the department cleared the men, and said no disciplinary action was necessary, the final judgment made clear that their conduct had on occasions fallen short of the levels expected and that the behaviour of Cummings and Frayne, who has since left the department, "has been perceived as intimidating". After the internal investigation was launched in the spring of 2012, the civil servant also decided to lodge a case with a tribunal, where the allegations would have been heard in public. A date was set for last month, but after further negotiations the financial settlement was agreed and the tribunal was cancelled.

On 23 January, however, Gove – who under the ministerial and special advisers' codes is responsible for the behaviour of his advisers (known as Spads) – denied knowledge of any allegations of misconduct during an appearance before the education select committee.

Labour MP Ian Mearns first asked him about "previous allegations about Spads acting inappropriately". He asked: "Are there elements working within the department that are out of control, secretary of state?" Gove answered: "No."

Mearns asked: "Categorically, absolutely not?" Gove replied: "I am not omniscient, but I have seen no evidence of that." Mearns then asked: "Are you aware of allegations of Spads acting inappropriately to civil servants within the department?" Gove answered: "No."

Labour sources said that it was almost inconceivable that Gove could not have known about the case and the payout. The Observer also understands that last year more than a dozen more junior officials lodged a "collective" grievance procedure and many later left the department.

Stephen Twigg, the shadow education secretary, said: "These are incredibly serious allegations. It appears that Michael Gove has either misled parliament or appears to have no control or knowledge of what his advisers do on his behalf. Either would be a breach of the ministerial code. We need a full investigation by the cabinet secretary."

Mearns told the Observer that there was a case for Gove to be recalled to the committee: "Clearly there is a case for the secretary of state to come back to the committee and answer further questions. He has either misled the committee or is the most ill-informed minister in the government." The DfE said: "It would not be appropriate to comment on individual employment matters." There was no response from the education secretary or the individuals involved.

The claims that Gove may have misled parliament follow a torrid week for the education secretary, during which he was forced to abandon his controversial plans to reform GCSEs.

Last weekend, the Observer named Gove's special advisers, Cummings and Henry de Zoete, who the secretary of state described last year as the "real heroes of reform", as contributors to an anonymous Twitter feed called @toryeducation, which attacks journalists and political opponents, in contravention of the special advisers' code. Documents relating to the grievance procedure involving Frayne, Cummings and others, seen by the Observer, show the complainant depicting the department as a place where foul language is commonplace and power is centred on a small group. Frustrated by delays, on one occasion Frayne allegedly snapped: "Just let's fucking do it." Cummings denied swearing at the complainant but did not deny swearing in the building.

The complainant alleged that Cummings undertakes "random acts of verbal aggression", being rude and threatening. Cummings recognised in his evidence that his behaviour in one meeting might have been perceived as aggressive, while pointing out that he was expressing frustration at what he thought was poor work. The complainant, who still works for the department but is considering early retirement, has suffered health problems, acknowledged by the department as the result of the events.