UK Regs do allow cable to be protected by fusing at the far end under certain circumstances - I'm not sufficiently familiar with the details to know if this would apply here.
This is exactly what applies here, and why 2.5 mm
2 spurs are allowed on a 32 A circuit. You have to separately meet these two criteria:
1. Protection against overload unless the load by its nature can't fail so as to produce overload. This can be at any point, so it is met by a downstream 13 A or smaller fuse.
2. Protection against short circuit, assumed to be a zero-Ohm short at the most distant point.
There are some assumptions baked into this, but the end result is you can take a 13 A rated flex* off a 32 A circuit to feed the hob, and connect the hob via a FCU** or a 13A plug, (probably with a 3 A fuse, that's plenty***, but you may be able to get away with higher). That fuse protects the cable against overload, because if some weird fault were to make the hob igniter draw say 20 A the fuse would blow before the cable is damaged. Separately, if a short circuit were to occur at the last point in that cable before the fuse, the total loop resistance (external supply impedance + 6mm cable + flex) needs to be low enough that the 32 A MCB would trip quickly enough to protect the cable. You check this by looking at the expected fault current, and corresponding max tripping time, and then you can work out the let through energy and the maximum temperature the cable gets to. You or your electrician should do this calculation, but in practice you'll find it is fine for sensible lengths of flex (too long and the MCB trips too slowly and the let though energy and final temperature is higher).
UK wiring regs are like this, you're expected to do actual engineering calculations rather than the US "rigidly follow code" approach. There are upsides and downsides to this.

Also, why not reduce the MCB feeding the 6mm cable to 16 A anyway? You may find the manufacturer's instructions (which you're supposed to "take account of") require that anyway, and that is a cheap and straightforward job.
*Why flex here though? A bit of 1.5 or 2.5 mm
2 T&E to a FCU would seem more conventional. If you do use flex you should really use ferrules.
**FCU = fused connection unit. It's a thing we have in the UK that takes the same type of fuses as the plugs but is for permanently installed things.
*** These ignition things take a couple of milliamps.