The Mail Online article included 58 separate images of Lordan, 51, which showed the star appearing to drink from a bottle of wine in the street.
The actress, who played Lynne Hobbs in the BBC soap, has spoken in the past about her alcohol use and was previously found guilty of drink-driving.
The charity Alcohol Concern told HuffPost UK that the coverage, which included a print article in Monday’s Daily Mail, was “unkind and intrusive”.
And press watchdog Ipso confirmed to HuffPost on Monday it has so far received 13 complaints over the Mail’s articles.
But after HuffPost approached the Mail for a statement about the piece, the website article was updated and 26 images of Lordan were removed.
Many of the images that disappeared from the page were close-ups of Lordan appearing to drink from the bottle. The edits left 32 paparazzi shots of the actress still published on the site.
The online article provoked a backlash from readers, one of whom commented: “Actually felt very uncomfortable reading this and the pictures were more than intrusive. Sad, all round and I am sure the family would prefer not to be in print.”
If anything Backgrid encourage... picture stories like this Backgrid photo boss David Taylor
The images were supplied to Mail Online by Backgrid, described as a “celebrity news agency”.
Its CEO, David Taylor, defended the images. He told HuffPost in a written statement: “If anything, Backgrid encourage[s]... picture stories like this. Not for the reason of just making money out of selling pictures, but also to bring to the attention of those close to the subject a cry for help.
“There is very little doubt that we are all off the assumption the subject needs help.”
Taylor said Backgrid “operates within the confides (sic) of the law” and pointed out the photographs were taken in a public place.
The Mail Online ran the photos under the headline: “Former Eastenders star Elaine Jordan, 51, sparks concern as she drinks in the street”. The Daily Mail newspaper used two images in print on Monday. The Sun newspaper also used two images but did not cover the story online.
Lordan’s time in the public eye has been marred by personal tragedy - her mother and her one-year-old son passed away within months of each other in 2005. Her stint on Eastenders was dogged by press speculation about her health.
Lordan herself alluded to excessive drinking during her rise to fame in a 2008 autobiography, Whatever It Takes. “I’d hang out with friends, knock back too much vodka and sometimes make an exhibition of myself,” she wrote.
“Nobody took any notice until my face started to be familiar on the box then I - just like other people in the public eye - became newsworthy.”
Substance abuse charity Addaction said that the media “can help decrease stigma by choosing words and images more carefully and humanely.”
Dr Richard Piper, CEO of Alcohol Concern, warned of the negative effects of media coverage and alcoholism. “While we don’t know Elaine Lordan’s circumstances, there are almost 600,000 alcohol dependent people across the country in need of help, and one of the reasons that fewer than one in five sought help last year is because of the stigma people who drink too much face.
“Our message is this: if you are suffering as a result of your own or others’ alcohol use, you need and deserve support. It’s the responsibility of all of us to challenge the stigma surrounding alcohol when we see it.”
Karen Tyrell, a director at Addaction, added: “Too often we judge without knowing the full story.
“It leads to people feeling isolated from society. People don’t develop drug or alcohol problems in a vacuum. Deprivation, poverty, trauma and poor mental health are all part of the equation.
“But a lack of understanding of these circumstances minimises public empathy and ultimately public support.”
The Daily Mail and The Sun declined to comment. Mail Online did not respond to a request for comment.
A representative for Lordan did not respond to requests for comment.
If you need help with a drinking problem, call the Alcoholics Anonymous national helpline for free on 0800 9177 650 or email email@example.com. For advice on how to reduce drinking, visit Drinkaware’s website or Alcohol Concern. Find alcohol addiction services near you using this NHS tool.