Boris Johnson has threatened to “privatise the arse” out of the Passport Office if it cannot clear its backlog and deliver better value for money, a senior Government source has said.

The Prime Minister also put the Driver and Vehicle Licensing Agency (DVLA) and other “arm’s length” bodies on notice in comments to Cabinet ministers, according to the source who attended Tuesday’s meeting.

Mr Johnson is understood to be “horrified” at the backlog in dealing with passport applications and will summon the agency’s leadership for urgent talks at No 10 on Thursday.

He is said to be concerned that families wanting to go on summer holidays are under pressure to pay up to £100 extra per passport for fast-track applications because of delays.

The source cautioned that privatisation would not be the starting point, but warned that Downing Street could look to businesses to take over if passport bosses could not meet the 10-week target for standard applications costing £75.50.

Mr Johnson was also said to have criticised “post-Covid manana culture” at some of the bodies for not adapting after the easing of coronavirus restrictions.

As well as the Passport Office, MPs have been raising concerns over significant delays in turning round applications for licences at the DVLA.

The Prime Minister is adamant this is a serious issue facing families and it's one that needs to be gripped

Downing Street chief of staff Steve Barclay is expected to meet with the Passport Office official later this week.

The Prime Minister’s official spokesman would not comment on Cabinet leaks, but told reporters: “The Prime Minister is adamant this is a serious issue facing families and it’s one that needs to be gripped.

“That’s his focus and he is ensuring that those responsible will be asked to make sure they are doing everything possible to clear this backlog and help hard-working families get their passports, get on holiday.”

In response to the criticism, a spokesperson for HM Passport Office said: “Since April 2021, we have been advising people to allow up to 10 weeks when applying for their British passport as more than five million people delayed applying due to the pandemic.

After two years of lockdown, we need to make sure people can have a good holiday ... making the most of the summer is vital

“We urge people who need a new passport to apply for one as soon as possible, with the vast majority of all passport applications being dealt with well within 10 weeks.

“To deal with this demand, we have increased staff numbers by 500 since April 2021. This has helped us to handle more applications than ever before, with more than one million passport applications processed in March 2022.”

Heathrow Airport chief executive John Holland-Kaye said it was “vital” that people could go on holiday this summer in case the UK reintroduced coronavirus travel restrictions.

Mr Holland-Kaye told the PA news agency: “Normally the Passport Office is very slick in processing passports. It’s really disappointing to hear (about delays).

“If it’s not resolved, it is going to mean that people can’t get away.

All our constituents are having to cancel holidays, miss funerals, rearrange visits, with even a new 10-week target routinely being failed. What will be done to avoid this predictable mess getting worse?

“After two years of lockdown, we need to make sure people can have a good holiday because many of them have vouchers that they’ve been saving up, they’ve got trips of a lifetime that they’ve put on hold, and we don’t know when things might get closed down again.

“Making the most of the summer is vital.”

The PCS union condemned the Prime Minister’s suggestion that HM Passport Office could be privatised.

General secretary Mark Serwotka said: “It is absurd for Boris Johnson to threaten to privatise HMPO, when it is clear that the current problems are mainly down to the casualisation of the workforce.”

For Labour, shadow home secretary Yvette Cooper said: “It’s disgraceful that families are having to cancel hard-earned holidays costing thousands of pounds because of chaos and delays at the Passport Office.

“Home Office ministers were warned many months ago that they needed to prepare for an increase in demand after Covid, but they have completely failed to do so and families are paying the price.”

On Monday, the Commons heard about one woman who had waited more than five months to receive her daughter’s new passport, with services branded “either really very good or an absolute shambles”.

SNP home affairs spokesman Stuart McDonald said: “All our constituents are having to cancel holidays, miss funerals, rearrange visits, with even a new 10-week target routinely being failed.

We would advise people this is a very, virtually unprecedented surge in demand, and if people are planning to travel this summer we would advise them to get their application in as soon as possible

“What will be done to avoid this predictable mess getting worse? And can we be assured that the 10-week target will not be lengthened further as we approach the summer?”

Home Office minister Kevin Foster said: “We don’t have any intention to further extend that standard.

“We are at the moment processing most passports well within it, but we would advise people this is a very, virtually unprecedented surge in demand, and if people are planning to travel this summer we would advise them to get their application in as soon as possible.”

He said the Passport Office dealt with a million applications last month, compared with seven million per year before the pandemic.

Conservative MP Simon Hoare described the backlog as “unprecedented, true, but foreseeable, absolutely”.