Quakerism started in England in the second half of the 17th century, during the aftermath of the English Civil War; a time when many people were interested in radically reshaping religion, politics and society. Early Quakers started preaching around the North of England, and then further afield around Britain, gathering followers who were convinced by their radical ideas.
One of the earliest recorded meetings was at Balby, near Doncaster, where George Fox himself preached.
The present Sheffield Meeting House was built in 1989. The previous Meeting House (currently not in use at all) is just a short walk away, close to the road called MeetingHouse Lane. Quakers have worshipped within this area for hundreds of years.
You can find much fuller history of Quakerism here.