How to prepare a concrete porch floor before tiling?

I’ve had an old UPVC porch replaced with a larger unit (about 1.9m x 1.4m internal). The porch is sitting on a concrete plinth that’s been present for years (i.e. it’s not a recent pour).

Half the floor area of the new porch is about 15mm higher than the rest, due to the mortar that was used to lay the previous tiles. So far it looks as though it’ll be tough to remove. The other half is bare concrete.

I want to tile the floor, but we’re planning on leaving a pram, kid's car seat, boots etc. in the porch, so I’d like to try to minimise damp if can.

I was wondering about laying a damp proof membrane, then tiling on top – but from what I’ve seen the membranes are designed to have a decent amount of concrete over the top.

Someone suggested I could seal the concrete with a suitable paint, and then pour a levelling compound/screed before tiling – but I’m not sure what product would be suitable (and compatible with a screed). Also, many of the levelling compounds I’ve seen are rated for indoor use, so I’m presuming a porch is probably pushing my luck a bit.

Alternatively, am I wasting my time trying to put down some sort of damp proof seal between a concrete floor and tiles in a porch? I.e. is it not really going to make any difference, and I should just level the floor and tile?

The concrete’s now quite mucky (unfortunately it was raining when the porch was installed) and it’s of course going to be pig to clean without making a mess of the inside of the porch (I can’t just hose the floor). As such, I’d need products that would cope with a bit of dirt on the concrete.

Any suggestions for suitable products/techniques gratefully received!