Hi the answer will depend upon distance from consumer unit, if not too far then 4mm2 cable on a 20A fuse/CB may do but as installing a new circuit & in a kitchen both mean part-p reporting to building control & the fact you are asking says you are not registered. Therefor probably cheaper to get registered leckie to do it for you,
4.3kw = 18.7 amp and 6 mmÂ² is rated at 23.5 amp to 35 amp according to how it is run so is ample for the electric oven. A 20 amp fuse or MCB will also be ample normally the manufacture will say what fuse should be used at the moment we are still on 16th Edition but to comply with 17th Edition if feed buried in the wall ceiling or floor at less then 50mm either flexishield cable if no RCD protection, or twin and earth with RCD protection from consumer unit to cooker point and 318B LSZH insulated/LSZH sheathed 300/500V to HO5Z1Z1-F 6mmÂ² cooker point to oven. The cooker point should not incorporate a 13 amp socket if it is not RCD protected. There are 45A Cooker Outlets which will allow you to feed the cable from the cooker point to a point closer to the oven buried in the wall and only close to the oven will the more flexible higher temperature 318B cable needs to be used. Depending on manufactures recommendations you may not be able to power the hob and oven from the same supply as some manufactures stipulate supply sizes so each will need its own fuse or MCB.
In real terms what I have said is rarely done, and the whole lot is feed in 6mmÂ² twin and earth throughout on a 40 amp MCB. The installer crosses his fingers that no pedantic inspector will pick him up on it. You may come under Part P as most kitchen work does and you will need to complete the installation or minor works forms, which means in real terms far easier to get a Part P registered electrician to do the work then try to jump through all the hoops required to DIY. There are links to Part P on projects page. Not to comply with Part P could cause problems when selling the house and also if anything goes wrong insurance as well. Although in theory you still can inform the council and DIY it is likely their inspectors would be pedantic.