Others have pointed out that's not enough money to replace welfare. Much of that money is spent on rubbish like donkey sanctuaries and other similarly thinly veiled cons, so it's not even equivalent. To add insult to injury, charities are exceptionally inefficient, so the overall cost to society for the same quality of life will be even greater.
Never mind the fact that without safety nets, people will have to weave their own. With employment rights thrown out the window, they'll by necessity have to be even stronger and more comprehensive. Instead of giving money to charity, they'll start stockpiling it against the bad times.
People never think it through - as well as fluffy happy commie reasons for benefits, there are plenty of good *right wing* reasons to maintain the benefits system. Would you want to work with benefit scroungers? Do you want them stealing your TV? Do you want to pay even more to put them in prison? Do you want them dying in the street from diseases they can't afford to treat, causing a massive public health hazard? Benefits are a really cheap way of keeping them in their place.
Even if we come down to libertarianism, the argument's flawed. How can there be the honest promotion charity really be born out of a doctrine that can be summed up as "Wahwahwah! I'm a selfish bugger and don't want to pay my taxes!"?