yoyo42 wrote:

What's the difference between a built-under and built-in oven?

I would say none, you might need to put some support cross-pieces in the
unit at a suitable height.

that would mean there was a vertical wall of vinyl-wrapped MDF right
next to the hob. Would that need a splashback or something similar to
protect it from the heat?

I believe you need a 50mm gap even for non-combustible materials

http://www.hse.gov.uk/gas/landlords/1-april-2009-tb-022-installation-of-previously-used-domestic-gas-cooking-appliances.pdf

Unless you still have the installation instructions for the hob and it
says different ...