The thing is people would still shop around for the lowest price. The vendor with the lowest price gets the business. Even opec can’t raise their prices in unison without someone cheating.
But we know economically this isn't necessarily true. Some industries are more monopolized than others. Some people aren't in areas where they have good alternative shopping choices. Goods like toilet paper have many different price points and it hasn't been a race to the bottom among the brands to become the cheapest toilet paper. "You get what you pay for" is still a common rule of thumb. Veblen goods would also rise in price.
It's my opinion that UBI would give businesses an opportunity to raise prices in certain sectors, but I concede it wouldn't be universal inflation across the board.
Competition will eventually drive prices down and lead to more consumer choice.
When everyone gets $1000 for sitting on their ass, wages have nowhere to go but up. Why go to work for minimum/low wage, if basic needs are met? Wages go up + inputs go up --> end prices go up --> even the "vendor with the lowest price" is charging much more than before.