Dame Louise Casey has "stepped back" from her role as the government's chief advisor on homelessness.
She was appointed in February to carry out a review, but the coronavirus outbreak saw her redirected to lead the government's homelessness task force.
Housing Secretary Robert Jenrick thanked Dame Louise for her work, especially around Covid-19.
But homeless charity Crisis urged the government "not to leave a leadership vacuum" after her departure.
The charity's chief executive, Jon Sparkes, said Dame Louise had made "extraordinary progress" in her role, adding: "With the economic impact of the pandemic pushing more people into homelessness, we must redouble our efforts, otherwise we risk rates of rough sleeping rising with all the human misery this entails."
The BBC's chief political correspondent, Vicki Young, said the former Victims' Commissioner was known for her straight talking and had not always seen eye-to-eye with the Conservative government.
It is understood Dame Louise would consider returning to lead the rough sleeping review later in the year, but only if there was a broad remit to consider all aspects of homelessness.
She has also been appointed a crossbench peer in the House of Lords.
In a letter announcing her decision, Dame Louise said: "Accepting the crossbench peerage is also a big deal to me and I want to think about how best I can make my contribution to public service from there.
"So for a number of reasons this seemed like the right moment to step back, especially as the country looks to gear up to the 'new normal'."
Labour's shadow housing secretary, Thangam Debbonaire, said Dame Louise's decision to step back "raised serious questions" about the government's strategy on rough sleeping.
She said the "chaotic government" had "no plan to avoid a self-made homelessness crisis this winter" - calling on them to extend the ban on evictions, brought in during lockdown, and to "come forward with a credible plan to keep their promise that no renter will lose their home because of coronavirus".
Dame Louise was appointed by Prime Minister Boris Johnson six months ago to head up the review into homelessness, saying he was "absolutely determined to end rough sleeping once and for all".
He put a deadline on this pledge of the end of this Parliament in 2024.
But when the pandemic hit the UK, Dame Louise became the head of the government's homeless Covid taskforce, organising emergency housing for almost 15,000 rough sleepers during lockdown.
Housing Secretary Mr Jenrick praised her work throughout the pandemic, saying it had led to "so many rough sleepers being helped off the streets and kept safe from coronavirus".
He added: "Her work leading the Rough Sleeping Taskforce will ensure as many people as possible who have been brought in do not return to sleeping rough."