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I'm not a structural engineer but generally any extension needs foundations into the ground to whatever depth is required by the SE/Building Regs Inspector. Ground conditions (soil type etc) , tree positions, the design of the extension, how it joins to the existing house - where the loads fall will be affect the foundation design.
Typically it would be a concrete trench but other designs might me used (mini-piles and a ring beam or possibly a concrete "raft").
On a slope - the external walls will be built up from external ground level and you'd probably use a suspended concrete beam and block floor to line through with the existing kitchen.
The BBC thing is too vague to judge but it seemed the motivation (cost saving) was primarily to do with creating a void for reworking drainage above 'ground' rather than having to dig it all in. Your sloping site might give you that option.
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Sheppz
Is it wishful thinking to hope that because my house is on a bit of a slope and the kitchen is a bit raised from the garden then I might be spared some of the costly groundworks on a future extension.
Standard Victorian semi... kitchen is a few steps down from the rest of the house then has a 1ft step out/down into the garden (and 2ft of crawl space underneath the floorboards).
Partner had an extension finished recently and some of the costs were fairly eye watering, but then she was extending a lower ground floor, in an older terrace with literally no foundations to speak of. Mine I would hope would be far more straightforward in terms of access and the amount of 'prep' needed.
The link @hugo7 posted (http://www.bbc.co.uk/iplayer/episode/m000wvy2 at ~29:30) where BBC architect suggested essentially a 'cheap' raised base sounds feasible to me.
Not to actually have a raised extension, but just bringing the extension floor up to the rest of the kitchen floor level.
Though I have no idea what I'm talking about.