Babylon Health acknowledged that its GP video appointment app suffered a data breach.
The company was notified of the problem after one of its users discovered that they had access to dozens of video recordings of other patient consultations.
A follow-up check from Babylon revealed that a small number of other UK users could also see each other's sessions.
The company said it had resolved the problem and informed regulatory authorities.
Babylon allows its members to speak to a doctor, therapist or other health specialist via a smartphone video call and, if appropriate, sends an electronic prescription to a nearby pharmacy. It has over 2.3 million registered users in the UK.
Leeds-based Rory Glover accessed the service by joining a private health insurance plan with Bupa, one of Babylon's partners.
On Tuesday morning, when he went to check a prescription, he noticed that he had about 50 videos in the consultation Replay section of the app that didn't belong to him.
Clicking on one of them revealed that the file contained footage of another person's appointment.
"I was shocked," he told the BBC.
"You don't expect to see anything like that when you use a reliable app. It's shocking to see that such a monumental mistake has been made."
Glover said he warned a work colleague of the fact that he worked for Babylon. In turn, he reported the problem to the company's compliance department.
Shortly thereafter, Glover's access to the clips was canceled.
London-based Babylon has since confirmed the violation.
"On the afternoon of Tuesday, June 9, we identified and resolved a problem within two hours whereby one patient had access to the introduction of another patient's consultation recording," he said in a statement.
"Our investigation showed that three patients, who had booked and had appointments today, were incorrectly presented, but did not see, records of other patient consultations through a subsection of the user's profile within the Babylon app.
"This was the result of a software error rather than a malicious attack. The problem was quickly identified and resolved.
"Of course we take any security concerns, however small, very seriously and have contacted the patients concerned to update, apologize and support where required."
A spokesman said that Babylon's engineering team was already aware of the problem before he was contacted by Glover's workmate.
He said the problem was accidentally introduced via a new feature that allows users to switch between audio and video consultations during a call.
And he said Babylon had informed the Commissioner's Office for information on the matter.
"The affected users were only in the UK and this did not affect our international operations," he added.
However, Glover said he still has concerns and doesn't want to use the service again.
"It's a doctor-patient confidentiality issue," he said.
"You expect anything you say to be private, not that it's shared with a stranger."
