Away from the challenges of Brexit, Boris Johnson is also under pressure over his friendship with a US businesswoman called Jennifer Arcuri.
The PM is being investigated for an alleged conflict of interest, but denies any wrongdoing and insists he acted with "full propriety".
So, what exactly is the row about?
What is Boris Johnson alleged to have done?
The matter revolves around the prime minister's ties with Jennifer Arcuri and whether she received favourable treatment during his time as mayor of London.
According to the Sunday Times, which first reported the story, the technology entrepreneur was allowed to join him on overseas trade missions in 2014 and 2015.
The newspaper said one of her businesses had received £11,500 in sponsorship money from a mayoral organisation when Mr Johnson was mayor and a £15,000 government grant for foreign entrepreneurs in Britain.
Mr Johnson is accused of not declaring a personal interest despite the pair having a friendship.
However, he has denied any wrongdoing. The prime minister says there was "no interest to declare" and everything was done "entirely in the proper way".
Ms Arcuri has refused to say whether she was in an intimate relationship with Mr Johnson. She said he was just "a really good friend" and "categorically" had "nothing to do with my other achievements".
She said they had never discussed sponsorship or grants and Mr Johnson.
A further £100,000 grant was awarded to Ms Arcuri's company, Hacker House, by the Department for Culture, Media and Sport in January. A subsequent government review said the funding was "appropriate". On 31 October, Culture Secretary Nicky Morgan said there was "no impropriety in the awarding of the grant".
Who is looking into the matter?
An investigation into the allegations was launched by current London Mayor, Sadiq Khan.
The Greater London Authority (GLA) - which consists of the mayor of London's office and the 25-member London Assembly - is looking into the matter.
The Assembly's oversight committee asked Mr Johnson to explain his relationship with Ms Arcuri, including a timeline of all contact.
It received a response from Downing Street, in a letter marked "confidential and not for publication". However, on 9 October, the committee said the letter failed to answer their questions.
Len Duvall, Labour chairman of the committee, says it's now deciding what to do next.
The oversight committee has the power to summon Mr Johnson in person should it want to. It previously quizzed him over a failed £53m project to build a "Garden Bridge".
In addition, the GLA's monitoring officer made a referral to the police watchdog on 27 September.
Its letter asks the Independent Office for Police Conduct to assess whether Mr Johnson has committed a criminal offence of misconduct in public office.
The GLA's Code of Conduct says public-office holders, including the mayor, should not act in any way to gain benefits for families or friends, and should declare private interests to resolve any conflicts.
Who is Jennifer Arcuri?
Jennifer Arcuri describes herself on Twitter as an entrepreneur, cyber-security expert and producer.
She began her career as a DJ on Radio Disney, before moving into film - where she wrote, produced and directed a short sold at Cannes Film Festival.
Ms Arcuri then created a streaming platform for independent film-makers.
But it was her founding of The Innotech Network in London that saw her path cross with Boris Johnson. The network hosts events to discuss technology policy and Mr Johnson was the keynote speaker at the first of those, in 2012.
Since then, Ms Arcuri has also another company, Hacker House, which uses ethical hackers to find technology solutions for businesses.
- 22 September: The Sunday Times publishes allegations about Mr Johnson's friendship with Ms Arcuri
- 24 September: The London Assembly gives Mr Johnson 14 days to provide "details and a timeline of contact" with Ms Arcuri
- 27 September: The monitoring officer of the Greater London Authority refers Mr Johnson to the Independent Office for Police Conduct
- 29 September: Mr Johnson denies any wrongdoing and tells BBC News everything was done "with full propriety"
- 7 October: Ms Arcuri tells ITV's Good Morning Britain programme she "never spoke" to Boris Johnson for help to secure any grants or sponsorship for her company
- 9 October: The London Assembly says a response it received from Number 10 does not answer its questions
- 31 October: Government rules the £100,000 grant given to Jennifer Arcuri's company was "appropriate"