Running power to a kitchen island

Use a flush mounted outlet or jbox, no sense having surface mounted on a floor. For cutting the chase, a wall chaser captures its own dust, an angle grinder doesn't, and the dust produced tends to be severe.

NT

I just figured it'd be easier - no need for a cutout (beyond that for the cable itself) and no downside given that both ends will be in the 6" void under the cupboards.

Note that the socket outlet won't be in the floor - I'll be sinking that into the side of the cupboard.

I've once seen power to to a kitchen island come down from a ceiling inside of a chrome pole.

There's a problem with kitchen islands. You have to walk around them. They are vanity items.

The main essence of kitchen layout is to have the sink. fridge and cooker close together.

You could well have a beam and block floor. If so, there should be ventilation bricks in the exterior walls below floor level.

In our our case it has been essential to give us sufficient worktop space given the size, shape and layout of the room.

Yes, we've got that but that's only a basic starting point. Workflow is much more than that triangle.

Yes, we have. Are you suggesting I route the cable under the beam and block?

A length of conduit will be fine.

:-)

I was wondering when you would spot that.