Step or slope over cavity into new extension?

[Em01]

Hi all, we’ve had a new extension put on the back of our kitchen and I am now left with a problem step as the floor level of the extension is 10 cm higher than the kitchen floor. The kitchen has an original 1930‘s quarry tile floor which we want to keep. Does anyone here have an inspired idea on how to bridge the gap? I’ve considered making a concrete step (not exactly sure how though) or having a slope (suggested by our quartz worktop fitter who reckoned a granite slope with anti skid ridges could work?)
The step/slope has to go over the old cavity wall. I have cleared the demolition debris out of it and now I seem to have hit soil is that probable/ok? What should I fill the cavity with, would foam gap filler be ok?
Any ideas would be greatly appreciated!! I have been procrastinating over this for weeks and need to sort it. Thanks! I attach some pictures

 

[Notch7]

its a bit late to ask why it was made higher -usually a FU in setting out levels.

You need some DPM to wrap into the cavity so that the plastic comes up to high enough to cut off later
then bung some concrete in the hole -I would suggest that will cause a thermal bridge but I guess the original floor has no insulation anyway.

I suppose you could concrete and finish a bit lower, allow to set then do some screed which you can finish to the slope you require.

 

[Em01]

its a bit late to ask why it was made higher -usually a FU in setting out

Yes I was surprised by the difference but it was matched to an earlier extension that adjoins on the left. It has left us with two big step ups, outside and inside

Anyway, thanks for the tip with the dpm! I cannot see any sign of any damp proofing around the perimeter of the kitchen, nothing in the cavity wall either. Should I still put dpm in the short strip under the door frame?