Let's say that currently rent is $1,000 per month, food is $500, and Alice is earning $2,500. Now UBI is implemented and Alice and all fellow citizens receive $1,000 per month. What will keep the market from easing the entry level rent up to $1,500 and food to $1,000 since the money is available? At first glance it seems like we'd just be choosing a different number representing "broke".
Imagine you're a landlord who runs a property for those of normal income. How much do you raise rent because people who currently earn below the poverty line suddenly have $1,000 extra per month? You can raise rent on everyone, but then most of your middle class tenants will move out to seek better prices. The same is true for the price of groceries and other staples.
A smart business will maintain their prices and benefit from a larger customer base. Since everyone doesn't experience an increase in income, raising rents of all forms will only open those businesses up to price competition.