The defence secretary, Ben Wallace, summoned senior generals to a rare special meeting of the army’s management board in London on Monday morning amid growing unhappiness about the service’s response to a series of scandals.

Allies of the minister said he had become exasperated after a series of bullying and harassment scandals, as well as allegations that a Kenyan woman was killed in 2012 by a British soldier whose identity is known to several colleagues.

The MoD said the hour-long meeting in Whitehall had been “full and frank” and that recent events had “brought to light important issues that require all our people to play their part in resolving”. It added: “The British army is only as good as the people who serve in it.”

Insiders said the tone of the meeting – attended by ministers and two-, three- and four-star generals – was largely constructive, and that the senior officers present had agreed with Wallace to address what the MoD described as “core and cultural issues” affecting the army.

No specific actions were cited, however, and the post-meeting statement also said the army would set out “exciting new plans for its future structure and deployments” later this month.

Two-thirds of women in the armed forces have experienced bullying, sexual harassment and discrimination during their career, a parliamentary report concluded this summer, warning also that the military is “failing to protect” female recruits.

It cited reports of gang-rape, sex for promotion and trophies or contests to “bag the women” on camp. Some women said they were bullied for refusing sexual advances, or had witnessed friends being attacked by groups of men but were too afraid to report it.

Since September, new army recruits have had to participate in sexual consent training provided by the Royal Military Police. But that requirement does not apply to existing soldiers, defence sources added.

On Monday night Sir Mark Carleton Smith, the head of the service, also announced the army would hold an independent audit of army culture to “reinforce the best and weed out the worst” as well as ensure better training and pastoral support.

In the past month, the army’s reputation has been damaged further after a press investigation into the unresolved 2012 killing of the 21-year-old Agnes Wanjiru, a Kenyan hairdresser who had turned to sex work to support her family.

The young woman was found dead in a septic tank near a British army based in the east African country, where she may have been dumped while still alive, after last being seen walking out of a hotel bar accompanied by a soldier in uniform.

A soldier confessed to her murder to colleagues, and his identity has been an open secret within the Duke of Lancaster’s regiment for years. But an investigation was only reopened by Kenyan and British military police in the last week.

Emma Norton, the director of the Centre for Military Justice, said the MoD needed to go further in dealing with bullying and harassment and allow civil authorities to take over all rape and sexual assault allegations, as well as introducing a central complaints team independent of each armed service to deal with serious harassment cases. “They know what they need to do, but they do not get on and do it,” she said.

The meeting also heard ministerial complaints about the ongoing noise and vibration problems with the next generation Ajax armoured fighting vehicle, which the MoD has expected to start taking delivery of this summer, but has now been indefinitely delayed amid accusations that its problems have been understated.

Further misconduct allegations will be aired in the high court on Tuesday, relating to the killing of four members of one Afghan family in 2011 in an SAS night-time raid. The deaths, described in one internal email as “the latest massacre!”, are among 33 suspicious killings involving the special forces in Afghanistan in 2011.