A Basic Income scheme would probably involve giving people Basic Income instead of other welfare payments and instead of tax allowances. For the population as a whole, it isn’t really ‘extra’ money. It’s just existing money which is being distributed in a new way.

I didn’t mean to come across snarky, but there was hardly call for that link to basic econ. I’ll see that and raise you.
https://www.amazon.com/Soft-Currency-Economics-II-MMT-ebook/dp/B009XDGZLI/ref=sr_1_1?keywords=books+warren+mosler&qid=1553646904&s=gateway&sr=8-1

If you prefer coursebooks.

https://www.amazon.com/Macroeconomics-William-Mitchell/dp/1137610662/ref=sr_1_fkmrnull_1?keywords=Macroeconomics+L+Randall+Wray&qid=1553648440&s=books&sr=1-1-fkmrnull

You do understand that tax policy cannot “distribute” anything, right? Taxation can draw down excess reserves and define deficits, but are never “revenue” to spend. If you are using them as inflation control there is some validity to limiting mortgage interest allowances etc, but the relationship is far from direct. You run into “propensity to spend” limitations when you go after stored wealth, whether it be in someone’s Treasury account or their home.