I’m not sure where this person got the 1511 date. I learned in grad school that the Poor Laws were Elizabethan in origin.
You can see a more detailed chronology with some of the key points of legislation at this pro-welfare-state site: http://www.workhouses.org.uk/poorlaws/oldpoorlaw.shtml
As you can see, nothing before 1601 called for any taxation. The 1601 legislation looks like it’s directed toward people who would fall outside the fraternal system. The taxation was done at a local level, as was the administering of assistance through the parish church.
Most conservatives and libertarians see the churches and voluntary associations as the appropriate dispensers of aid to the poor, and that’s what happened here. The complicating factor is that the Church of England was controlled by the state, so the argument can be made that there was a crowding-out effect on the church side.
The assertion that the Poor Laws were passed because “private charity didn’t handle the problem” is dubious. For one thing, the legislation doesn’t say that. For another, you could just as easily argue that the preexisting restrictions on the movements and wages of laborers created or exacerbated the problem of unemployment in various localities. In other words, the Poor Laws can be interpreted as a response to a problem previous legislation had created.