Which is why UBI should be coupled with UBS (universal basic services). In this context, at the very least there would exist also a rental board (like Quebec's existing Regie du Logement). If you're more ambitious, housing would be a universal service and taken out of the market altogether. And don't forget that that 1600E income of the landlord would be also taxed.

More generally: https://ubiadvocates.org/inflation-and-ubi-separating-fact-from-fiction/

If UBI is financed through measures that inject new money into the economy, such as deficit spending or monetary expansion, the risk of inflation may be heightened. This is because the increase in the money supply outpaces the economy’s capacity to produce goods and services, leading to a general rise in prices.

Conversely, if UBI is funded through redistributive measures, such as progressive taxation or cuts in inefficient spending, the inflationary pressures can be mitigated. By targeting resources from high-income individuals or unproductive sectors of the economy, such funding mechanisms redistribute existing wealth rather than injecting new money into circulation.

This ensures that the overall level of demand remains relatively stable, thereby limiting the potential for inflationary spirals.