New cooker needs wiring
You say you've got a 35A fuse and the unit takes 32A. So, on that front, you're good.
I'm not sure how UK wire is sold size-wise, but what you'll want to do is find some 3.5-4mm copper wire, which is rated for at least 40A (in the US we call it 8 gauge). It might be ideal to find it in a cable (hot, neutral and ground) for ease of running.