Three-year-old Alan Kurdi was found on a beach in Turkey.
His limp body had washed up in September 2015 after the boat carrying him and his family, including brother Ghalib, five, to Greece capsized.
Ghalib and the boys’ mother Rehanna also drowned.
Ms Kurdi, who is based in Canada, said: “The number of refugees is triple – every year it’s getting worse and worse.
“The international community, they fail to find a peaceful solution to end this refugee crisis, which is sad when every year I’m seeing the numbers go very high.
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“The suffering continues. We know every year people are desperate, they’re crossing that Mediterranean, they’re still doing it, three years later.”
Ms Kurdi, who has written a book about Alan’s death called The Boy On The Beach, believes the UK should act now.
She said: “If we’re going to look back a few years from now, we’re going to feel ashamed of ourselves if we don’t do anything.
“It wasn’t easy for me to share with the world my private family story.
“In some ways our private family story is one of many.
“I’m really hoping this story will let the people realise my people are not different to anybody else. We’re just people. We do everything everyone in the West does.
“Maybe we speak a different language, we practise a different religion, but we celebrate birthdays, holidays, we go to school, we go to work.
“We should invest and bring more people to settle in the UK, for example.
“Let there be private sponsors, like community charities, they can at least give that chance to give education to the children.”
Amnesty International has blamed the deaths of more than 700 migrants trying to enter Europe across the Mediterranean since June on the policies of EU nations, including Italy and Britain.
In a report published this month, the charity claimed 564 people were found dead or reported missing in June and a further 157 in July.
It is feared 500,000 Syrians have been killed in the seven years since the start of Syria’s civil war, while six million have fled the country.