Ms Bulley, 45, vanished after dropping off her daughters, aged six and nine, at school on January 27 in St Michael’s on Wyre, Lancashire.
Following a press conference in which they revealed Ms Bulley was classed as a high risk missing person Lancashire police released a statement saying that the mother-of-two has “some significant issues with alcohol” and “ongoing struggles with the menopause”.
The move has been highly criticised and Home Secretary Suella Braverman has demanded an explanation.
Asked by broadcasters what he thought of the information disclosed by the force, Mr Sunak said: “Well I agree with the Home Secretary, and like her I was concerned that private information was put into the public domain.
“I’m pleased that the police are looking at how that happened in the investigation.
“Obviously my thoughts are with Nicola’s friends and family and the focus must now be on continuing to try and find her.”
A source close to Ms Braverman told the Standard that she met with Lancashire Police Chief Constable Chris Rowley on Friday.
“Ms Braverman outlined her concerns over the disclosure of Ms Bulley’s personal information and listened to the force’s explanation,” the source said.
“The Home Secretary asked to be kept updated on the investigation.”
Information commissioner John Edwards will question Lancashire Police about whether releasing Ms Bulley’s information was necessary.
He told the Radio 4’s the World at One that information surrounding health was classed as “special category data” and was “treated to an even higher standard”.
Asked if it was against the law for police to disclose this information without sufficient justification Mr Edwards said: “Yes, that’s right.”
Mr Edwards said data protection laws existed “to ensure personal information is used properly and fairly”.
“Police can disclose information to protect the public and investigate crime, but they would need to be able to demonstrate such disclosure was necessary,” he said.
“We recognise that at this stage of an intensive, live investigation, the force must focus all their energies on the inquiry.
“But given the high profile nature of this case, we will be asking Lancashire Police to set out how they reached the decision to disclose this information in due course.”
Mr Edwards said he would not comment specifically on Lancashire Police, but to release personal information about a person’s health there “would need to be a really clear and demonstrable need and a clear link between that disclosure and a legitimate police objective”.
Former victims’ commissioner Dame Vera Baird accused the Lancashire force of making a “sexist” error in divulging the mortgage adviser’s vulnerabilities.
Ms Bulley was last seen at 9.10am walking her springer spaniel alongside the River Wyre. Her phone, still connected to a work Teams call, was found just over 20 minutes later on a bench overlooking the riverbank, with her dog running loose.
Dame Vera said the way personal information about Ms Bulley was given out was a “dreadful error”. She told BBC Radio 4’s Today programme: “A future family like this is going to face the torment of not knowing whether to run the risk of gratuitously wrecking your relative’s reputation by giving every detail away… or missing the chance of catching whoever has got them, or getting her back. So, I’m afraid this is the biggest error that I have seen for quite a long time. It’s going to just, you know, very sadly, undermine trust in the police yet further.”
Asked if it was an error that would have been made if the potential victim was a man, she said: “I do not think that it would. Would we have had police officers saying, you know, if it was Nicholas, he’s been unfortunately tied down with alcohol because he’s been suffering from erectile dysfunction for the last few weeks? I think not.”
A source close to the Home Secretary said she had received an explanation from police last night. The Home Office also said it was receiving regular updates from the force about its handling of the case — including “why personal details about Nicola were briefed out”.
Lancashire Police has referred itself to the police watchdog over contact they had with her prior to her disappearance. Ms Bulley’s relatives said people needed to stop “making wild theories up” about her private life and issued a direct plea for her to return, adding: “Your girls want a cuddle.”