overlaying 1 inch of concrete

There are some special screeds that can be used at that thickness, although they may not be available in your area.
http://www.screeds.ronacrete.co.uk/screeds/polymer-screeds/ronafix-pre-packed-screed-6-50mm

What we call a screed here is about 3 inch of sharp sand/cement laid semi dry on top of the concrete floor slab to get a really flat finish. Nowadays the insulation boards are often placed on the slab first and then the screed goes on top, but the insulation can go under the slab.
There are other screeds used now such as wet self leveling ones for underfloor heating, or thin ones.
However I agree that plywood is the easiest option for DIY, and also the cheapest.

Plywood is normally well screwed down on timber floors to make a solid base for tiling.
Years ago tiles were laid on a mortar bed, lime/sand and later OPC/sand. Wall tiles were also put on with mortar.
It does mean that a really uneven floor or wall can be made straight with this method.
I did use this method on my own house years ago when marrying up 2 concrete floors with 3/4 inch difference.