How to level a floor prior to laying parquet

Hi,

I have a floor a concrete floor that has had a skim coat applied to it by the previous owners.

The floor is not all that level and not all that even either.

I want to lay a parquet floor and as far as I can tell I have a few options.

1. Just lay the parquet, don't worry about the subfloor (worries it'll be gappy and reflected light after buffing will look bad).
2. skim/screed the unevenness out of the subfloor and just accept it's not level. Who cares after all?
3. Remove current skim and relevel the floor.

A part of me wants to pursue option 3.

The room is 5x7m but (16.5x23ft) but a bit of a wonky shape. My plan was to buy a long straight edge, then lay battens like tram tracks just a blt less than straight edge's width apart ensuring that the top of battens are level.

Fill between the battens with self leveller and smooth over the top of the battens.

Once complete I'd lift up the battens and repeat the process one straight edges width to the side.

It sounds like a lot of work but then again, a well laid parquet should be done for decades.

The only thing I am worried about is getting the battens level to start with, as from the shop they usually are not. On thing I thought of would be to use skirting board which I am lead to believe comes a lot straight from the get go.

What do you think?

First thing will be to moisture check the subfloor with a hydrometer or protometer. If moisture levels are dry and within tolerance of the parquet, lay a quality, moisture tolerant self leveller like Arditex Ardit NA, then lay the parquet to this.