The investigation will look at several issues including whether the relevant protocols were in place and applied correctly, whether there was sufficient staffing, and whether the terror suspect was held in the right category of prison.

Keith Bristow QPM, former director general of the National Crime Agency, has been appointed to lead the investigation.

Justice Secretary Alex Chalk confirmed the appointment on Twitter and that he wanted the findings to be published "promptly".

It comes as prisons minister Damian Hinds admitted that Wandsworth had staffing issues on the day Khalife escaped.

In a written ministerial statement, Mr Hinds said 1,594 prisoners were held at Wandsworth on 6 September, while 125 Band 3 prison officers attended their shift on that day - 61% of all staff due to attend.

He said overall staffing levels were above the minimum required to "deliver a safe and decent regime" - and an initial investigation concluded this was not a contributing factor.

But Rosena Allin-Khan, the Labour MP for Tooting - the constituency that covers Wandsworth prison - said she has had concerns "for many months" about staffing levels at the prison.

"This sits with the government. Their under-resourcing of the prison service has caused this," she warned.

Khalife, a former soldier, is suspected to have escaped by strapping himself to the underside of the truck to make his escape.

It prompted a 75-hour manhunt before he was eventually arrested and recaptured in a west London suburb.

Earlier this week, Khalife appeared in court charged with escaping from lawful custody.

Sky News understands he is now being held at Belmarsh, a category A jail.

In the terms of reference for the investigation, published by the Ministry of Justice, Mr Bristow will be asked to consider, among other things:

• Whether the relevant protocols were in place at Wandsworth and there was the means to apply them

• Whether there was sufficient staffing in place

• Risk assessments and decisions about employment in the prison

• How Khalife was able to access the materials that facilitated his escape

• Security measures including checks on the delivery vehicle that he used for his escape

Khalife's escape prompted a number of questions about the state of the UK's prison service and whether it could have been avoided.

On Friday, the Justice Select Committee announced it was launching a new inquiry into the future prison population and estate capacity.

The prison population is currently projected to increase to 94,400 by March 2025 - and a range of 93,100 to 106,300 by March 2027.

Last October, the government was forced to activate Operation Safeguard, in which up to 400 police cells have been used to hold people overnight due to a lack of space.

The government has also started rolling out rapid deployment cells to manage the demand for prison places.

Justice committee chair Sir Bob Neill said: "The prison population in England and Wales is rising and is forecast to increase even further. The temporary use of police cells serves to highlight the pressing need for the government to urgently address prison capacity.

"Overcrowding remains an issue within the prison estate - particularly in male local prisons - and the rise in the prison population may also aggravate pre-existing issues across the estate.

"Concerns have been raised over safety, the condition of old prison buildings and the lack of staff to safely manage and rehabilitate offenders."

In his previous roles, Mr Bristow was the former head of crime for the Association of Chief Police Officers and former chief constable of Warwickshire Police.

When he completes his report, it will be sent to Mr Chalk and the leading civil servant at the MoJ, Antonio Romeo.

The MoJ said: "Public protection is of the utmost importance and the purpose of the investigation is to identify shortcomings and ensure lessons are learned to help prevent incidents of this nature occurring again in the future."