I don't really understand what you mean, why do you need an income tax if you have a negative income tax.
Also it's not a major re-distribution of income, just enough to prevent a layer of society being in absolute poverty. It works within a free market system, and whilst far from being a perfect free market it does however appease the general population who by this point want some kind of social reform and avoids the creation of the welfare state; I can imagine any reformed classical liberals accepting it as the price for a continued domination of UK politics
A negative income tax is essentially an attachment on the progressive income tax that redistributes wealth from the top brackets down into "negative brackets" for the poor. If we're talking about a redistributive tax policy that's not attached to the income tax, then the proper term is a Guaranteed Minimum Income.
And a GMI has major implications for the free market. One of the conditions of a free market is that income is dependent either on wage income or capital gains - by creating a GMI, you reorient the relationship of income to labor in a fundamental way. This is going to have massive implications on unemployment and wages - many low-wage workers are going to quit their jobs rather than work themselves to the bone for a pittance; the number of applicants per job is going to shrink dramatically, which increases wages and provides labor with much more bargaining power.
A GMI isn't cheap either. Just taking the U.S for example, we have 13% of the population living in poverty (or 39 million people). To provide a GMI that brings people up to the poverty line, which is too low to begin with, would cost about $624 billion a year (39 million people times $16k for an average household of 2.59 persons).
You cannot fund a GMI without taxing wealth - whether we're talking about income, inheritance, property, or capital gains, the revenue has to come from somewhere. Which means we're shifting 4.4% of GDP annually from the rich to the poor - a classical liberal will tell you that this is an unconscionable attack on property rights.
But part of where I think you and I are at odds on this is what our definition of free market is. I would define the free market as commodification in land, labor, and credit without restriction or remediation from the government. If that's not what your definition is, I don't see why the welfare state should be any more of a divergence from the free market than a GMI, unless we're rather arbitrarily defining non-free market as "income transfer programs but only if they involve large numbers of administrators."
I'd also note that we're only talking about the welfare state here - how are we possibly going to avoid a regulatory state in the face of the massive social and environmental externalities caused by the industrial revolution? How are we going to deal with a rising union movement is at an ebb in 1929 at 29% of the workforce, and will by the late 30s return to growth and peak at about 50% of the workforce?