Assuming a competitive market, which is a decent assumption overall though clearly there are good for which it doesn't work, an increase in demand (which is what more money going to people more likely to spend it does) should result in an increase in price smaller in proportion than the increase in income and an increase in the quantity of goods sold. So, yes, you'd expect some inflation, but not so much (at any level) as to render the increased income useless.
If everyone knows they can get basic income for doing nothing, the majority will not choose a job that pays less than or equal to the basic income.
This means businesses will have to increase wages (and costs of goods and services). No colluding necessary..just economics.