joining wire for induction hob

[wildmetal]

hi looking to install a new induction hob to current wiring . the wiring i have is thick white probably about 15mm wide and is hard wired into current hob and isolation switch . now i don't really want to rip all the tiles off to get at the cable .and the new hob seems to have thinner wires like on a 3 pin plug . is there a way i can cut and join these together maybe a junction box