Scottish and English Building Control are worlds apart.
FWIW £1,000.00 sounds steep for a straight forward cut down with no structural works required.
Id suggest asking around for local Architectural Technicians, smaller the better, to quote.
If you decide to tackle the drawings yourself you’ll need sections through the slip step, jamb and possibly the lintel. Standard details were at one time available on the Scottish Building Standards website. Can’t remember if u-values will come in to it but you will need to detail external steps/plats and show how you’ll maintain subfloor ventilation if you obstruct any existing vents.
The good thing is that you’ll get a ‘faults’ letter detailing any lack of information in your drawings and it’ll reference the standard you need to satisfy. A bit of research will tell you how to meet the standard and it’s just a case of showing/detailing it on your drawing.
best of luck!