The Woolwich Free Ferry was established because of the protests of Woolwich residents. Most of London's bridges were private businesses that charged tolls from those that used them. This discouraged most ordinary people from using them unless there was no alternative.
In 1877, Parliament passed the Metropolis Toll Bridges Act. This allowed the Metropolitan Board of Works (the MBW - predecessor of the London County Council) to buy up the private bridges and abolish the tolls.
This angered the people of Woolwich, who still had to rely on the ferry. They pointed out that their taxes had helped to pay for these bridges, so they were subsidising free crossings in wealthy west and central London. They felt they were also entitled to a free crossing.