x-stor(e)y or x-floor or x-level house/building?

Which is the correct for British English? I need the correct for both a separate house and an apartment building, if this makes difference. I can't find any concrete answer online.

2-storey, 3-storey house; 80-floor skyscraper

Either "-storey" or "-floor" sounds natural in UK English.

"-storey" is particularly used for small numbers (such as 2 or 3), and for long term living accommodation (i.e. a block of flats/apartments).

"-floor" is most often used for large numbers, especially of an office building, hotel, or with the word "skyscraper".

"-level" is less common in general, except when it is describing something that would normally be expected to have only one storey/floor/level, but in this unusual case has two or more, such as a "2-level apartment". Indeed, it is more likely to be called a "split-level apartment", to emphasise the unusual splitting of an abode.

Incidentally the UK spelling is "storey" while the US spelling is "story". In both, the plural is "stories".

"Residents living in the shadow of Grenfell Tower have said they fear for their health after an independent study found cancer-causing chemicals near to the 24-storey block, which was destroyed by fire in 2017."

Source: The Guardian, 2019

They moved from a bungalow to a 3-storey house when they got married.

First floor

US and Canada count stories from 1 at the ground floor.

UK and Europe in general count stories (effectively) from 0 at the ground floor, although typically they name the ground floor just "Ground" rather than explicitly level 0. The first floor, in UK/Europe, is the floor immediately above the ground floor.