The woman, aged in her 50s, died after having been seen in the doorway of the Poundland on Castle Square, despite paramedics trying to save her.
Police said she was believed to have suffered a medical episode and died at the scene. Her death is not being treated as suspicious.
But this afternoon, officials from a charity set up to help the homeless called for an end to begging and blamed the problem for the tragedy.
He revealed the woman who died had refused to go to hospital despite being unwell because she expected to make money begging. And he added she was not homeless.
Tim Renshaw, chief executive of The Archer Project, based at Sheffield Cathedral, which works with homeless and vulnerable people, and also speaking for the Help Us Help project, said: “The tragic death last night highlights the concern that many agencies working with the homeless community have about begging.
"We don’t know if the death could have been prevented but we do know that the medics weren’t given a good chance to save life. And we know that if begging wasn’t profitable that person would have spent time with drug treatment services instead of hours sat in a doorway asking passers-by for money.
"Many will have assumed the person was homeless but they had a home. Their success in getting money through begging kept them away from that too.
"We know all of this because each day the various outreach teams talked with this person, offering the real support they needed, but the pull of money raised through begging was too strong. Not everyone on the street is an addict but there are many reasons why they might be, such as some form of childhood trauma or family break ups."
He said the woman who died would not go to hospital when she felt ill.
He said Sheffield city centre ambassadors were with her throughout the day and, and he understood they tried to get them to go to hospital.
But he said she had stayed in the doorway because begging would provide money to buy the drug spice, which she was addicted to.
Mr Renshaw said: “The drug dealers may have seen the events unfolding because their job is to sell the drugs, and this person was a customer. As ever, the dealers were nowhere to be seen when help was needed - they never are. A dead person can’t spend money.
“We appreciate that people do want to help, and how difficult it can be to resist giving money direct to those who are begging. However there are better ways to make a difference than giving money to people sat on the street.”
He urged people to support the local agencies which provide food, drinks, nursing and other medical support to change lives with organisations needing donations of money, food, toiletries and clothes, or consider volunteering.
Recent figures reveal five people died in Sheffield while homeless during 2020 – a fall from the previous two years. The figure for 2019 had been six, which was down from 2018, when 11 died while homeless.
Go to www.helpsuhelp.org.uk for details.