It's not clear that this will be enough to offset inflation, but the truly excellent Basic Income subreddit FAQs [1] addresses inflation specifically, and in essence there has been little to no evidence of it in practice.
I personally have always been a fan of Henry George who not just advocated an LVT, but suggested that this should be the only tax - all other taxes were unfair. I realise I am in a minority and some taxes can help with social/healthcare issues (e.g. on tobacco and alcohol).
That said, UBI with a rigorous LVT would be my ideal. Alas, voters utterly despise both, at least in the UK, so it's unlikely we'll see either any time soon.
I suspect many would head to sea/tree change if ensuring your earnings was not such an important factor.
Plug one hole in the dike and others will pop up. Just let the free market work and people choose where they want to live and work.
Whether or not there is a basic income, it's the right thing to do. Income should be either earned (by creating value) or shared equally (if derived from land and natural resources).
The government zones the way it does today on purpose, to create a built environment and social structure that insures you have to work all the time to afford housing and a car. This makes you docile and governable and taxable.
Basic income should be coupled with government initiatives to increase the supply of housing (eg. zoning and regulation changes to allow increased density, subsidizing non-luxury apartments, land value tax).