LONDON — As he finally moves into the job he has wanted all his life, the newly anointed prime minister, Boris Johnson, brings with him a formidable array of challenges, the most pressing being his promise to extricate Britain from the European Union.

He also brings a chaotic personal life and, as the first single prime minister in more than 40 years, an unsettled domestic situation unique in the annals of modern-day prime ministerial politics.

Separated from and in the process of divorcing Marina Wheeler, his wife of 26 years, Mr. Johnson has since last year been dating and intermittently living with Carrie Symonds, 31, a former spokeswoman for the Conservative Party. Ms. Symonds has been credited with getting Mr. Johnson, 55, to cut his hair, lose some weight, affect more gravitas and start wearing clothes that look to be ironed.

But the couple have not appeared at any public events or been photographed together since neighbors called the police last month to report that the two were having a loud argument at her apartment. (The police said they visited and there was no need for further action.)