Ben Wallace, Britain's security minister, told the BBC on Thursday that Begum could face prosecution if she returns Britain.
"I saw a beheaded head in the bins", Ms Begum said.
Speaking from a refugee camp in Syria, she said she had had two other children who both died over the last four years. The fate of the third girl is unclear.
Begum and two 15-year-old girls - Kadiza Sultana and Amira Abase - fled to Turkey from London in February 2015 after telling their parents they were simply going out. Abase and another woman who had fled from Bethnal Green two months before them, Sharmeena Begum, are most likely still alive in Baghuz, she added.
The US-backed Syrian Democratic Forces on Saturday launched a final push to expel ISIS fighters from the sole remaining morsel of the proto-state they declared in 2014 across parts of Syria and Iraq.
The 19-year-old said life under the Caliphate had been a normal one. She was then married to a Dutch fighter named Yago Riedijk, who was older than her by 12 years, according to Al Jazeera.
As the terrorist organization lost more and more ground against the various forces in Syria, the teen and her family moved down along the Euphrates river valley, finally ending up in the last bit of territory the group still controls, Baghouz.
"It was like a normal life. But other than that..."
"I was weak", she said. He said she would have known what she was getting into when she left London for Syria. "And I don't regret coming here".
Other options officials can consider include prosecuting Ms Begum in her absence for being in a designated terror area, or allow her to return.
Begum said she was nine months pregnant. There was so much oppression and corruption that I don't think they deserved victory.
She referred to her husband having been held in a prison where men were tortured.
Ms Sultana was reported to have been killed in an air strike in 2016.
"We stayed until we could find a window, then we took it", she said. At first I was in denial. As a family we can't understand how her head was turned like this and why she thought going to Syria was a good idea.
Ms Begum said losing two children "came as a shock". "It just came out of nowhere, it was so hard".
The first child, a girl, was buried in Baghuz a month ago at the age of one year and nine months.
The British among them divide neatly between the two.
She told the paper that "the caliphate is over". "There were no drugs available, and not enough medical staff", she said. "It is up to her to present herself at the British borders, for the future of her child".
"I was weak", she said.
"I could not endure the suffering and hardship that staying on the battlefield involved", the 19-year-old told the Times. She is now one of 39,000 people living in a refugee camp in northern Syria. "Now all I want to do is come home to Britain".
But he said hearing Shamima Begum's story gave him hope.
"I just want to come home to have my child".
Nigel Farage has given his damaging verdict on an ISIS bride who ran away to Syria and now wants to return to Britain.
"It is a challenge for all of us", he told BBC radio.
This undated photo issued by the Metropolitan Police shows Shamima Begum.
ISIS aims to create an Islamic state called a caliphate across Iraq, Syria and beyond.