Do you really need the 100mm step down?
https://forum.buildhub.org.uk/topic/2891-integral-garage/?tab=comments#comment-44265
A couple of quotes from the above thread:
"the garage floor can be level and the house level but there must be a height difference between the two, the height difference can be made up with a slope rather than a step"
"We have the same and have a 50mm fall in the slab towards the garage door over a distance of about 5m"