Is there nothing of the existing house that can be saved?
I'm not aware of a price or rate as such. It could be worked out as Hi Max + Driver by number of days required to demolish house & load rubble into trailers to be removed off site.
Digging up existing foundations would incurr a similar cost. Some Council might insist in all rubble being crushed on site by machine and filling re-used where possible.
ChecK with your Council, you may need permission as technically a newly built house, to wallplate level could be consider as a "Substancially complete dwelling". Such a dwelling could then be considered Habital and require permission to demolish. Worth a phonecall be L.A to be 100% clear.
Get at least 3 written quotes from 3 local Groundworks Contractors.