LONDON — Meghan, the Duchess of Sussex , said Friday that she was “deeply distressed” by a report alleging that her estranged father, Thomas Markle , possessed child sexual abuse images, and said that she was informed by police of “disturbing allegations” against him in 2018.

In a statement on Friday, Meghan addressed the report that her father was being investigated over claims he kept child sexual abuse images at his home in the Philippines.

The allegations were first reported by The Sun newspaper, a British tabloid, which reported that Markle’s son had informed police after finding finding a hoard of images. The Sun published a photo it said showed Markle’s son, Thomas Jr., as signing a sworn statement it said he had submitted to police and quoted Markle Jr. as saying: “I won’t speak to my father ever again unless I’m called to give evidence against him.”

Thomas Markle Sr. denied the reported allegations, calling them “sick lies” in a statement to Britain’s Daily Mail newspaper.…