Laying ceramic floor tiles in a kitchen?

Stu spake thus:

Yes; there's this stuff that in the US is called "wonderboard"; I think the official name is something like "fiberglass concrete board", or some such. About 1/2" thick, comes in 4'x8' sheets, cuts easily, serves as excellent underlayment for tile. But you *definitely* don't want to lay tile over floor boards directly; that's just asking for future trouble.

Talk to the tile store about a membrane. This is a thin sheet that goes under the tile and prevents movement under the membrane from being transferred to the tile. It is very common when tile is laid over "green" concrete that is probably going to crack. It isn't cheap

Mastic is somewhat flexible - much more so than the cementacious thinset normally used - but that doesn't matter...if the supporting surface (boards) flexes the grout between tiles will certainly crack and the tiles themselves may.

If the wood portion isn't suitable "as is" (probably isn't) and you want both areas to be the same height then you'll have to increase both areas by the same dimension; e.g., 3/4" ply + 1/2" cement board over both wood and concrete. If there is any bounce to the boards now you may well have to go thicker than 3/4" ply.

I had a problem with a floor that flexed in one area even after using the concrete backer board. Some of the original grout was cracking and coming up in this one area about a year after installation.

We took out the old sand grout in that area and replaced it with epoxy.

Schluter-Ditra is a product that supposedly eliminates cracking problems. It's maybe 3/16" thick, so your height problem would be minimized. Expensive though.