Two women are among the four senior officers to have been shortlisted to succeed Sir Bernard Hogan-Howe as head of the Metropolitan police.

Cressida Dick, a former Met commander currently working at the Foreign Office on secondment, and Sara Thornton, chair of the National Police Chiefs’ Council have made the list.

They are up against Mark Rowley, a Met assistant commissioner who leads on counter-terrorism across British policing, and and ex-Met veteran Stephen Kavanagh, chief constable of Essex police.

Candidates have already faced psychometric tests of close to two hours duration, which assesses their psychological make-up, personality and ability to take advice – the first time such testing has been used to help make the appointment.

The final decision will technically be made by the home secretary Amber Rudd, who must take into account the views of London’s Labour mayor, Khan. It is understood that meetings with those shortlisted were held last week with Khan.

Issues on the London mayor’s mind are how candidates would reform a predominately white force – which is also the largest police force in England and Wales, while growing consent from London’s increasingly diverse communities. These goals will have to be achieved against a need to find £400m budget cuts by 2020.

The selection of the Met commissioner involves several stages – and next week candidates will start to go before a panel for a full interview. Then the candidates will be whittled down, possibly to two, and go before a second panel consisting of the home secretary, the London mayor and the policing minister Brandon Lewis.

The choice is expected to be announced by late February. The Home Office wants a news blackout on the progress of the process, and declined to name those shortlisted saying that “applicants have a right to confidentiality”.

The candidates are vying to replace Hogan-Howe, who is the first Met commissioner since 2005 to complete a full five year term in office. Previous to him, Sir Ian Blair and Sir Paul Stephenson had both resigned mid-term after being dogged by controversy.

Sources claim the race is wide open and no decisions made despite some media claims the government wants Dick to be commissioner. The Met has never had a woman in charge since it was established in 1829.

Traditionally the commissioner of the Met was seen as the top job in British policing, and the force currently operates with 32,000 officers, one quarter of the total in England and Wales.

But that dominance is seen as being on the wane and one candidate who would have been favourite to become commissioner, Lynne Owens, chose instead to be director general of the National Crime Agency, which is informally described as Britain’s version of the FBI.

Some believe the Met should be stripped of its national responsibility for counter-terrorism and that should be handed to the NCA, allowing the force to concentrate on policing London. The Met leadership tends to oppose the idea.

In a Guardian interview last month, Thornton warned of tough choices ahead for policing as it balances competing and rising demands, amid tight budgets.

The post of Met commissioner carries a salary of £270,648 plus benefits and will be a five-year appointment by royal warrant. The advert for the post says candidates should “show evidence of successfully leading transformational change in a challenging financial climate”.

It also says those wanting the role must have “an understanding of changing crime and threat patterns”, a reference to the growing dangers of cyber crime, “and the protection of the most vulnerable”.

The Met was heavily criticised by the official police inspectorate for being substandard in child protection and within policing the growing need to protect the vulnerable from crimes such as sexual abuse is a growing challenge which requires changes in workforce, culture and ways of working.