From what can be seen in the photos, to comply with BS7671 & building regulations it will need (as a minimum):
1. RCD for the socket outlets in the kitchen - this could be added next to the existing fusebox.
2. Individual sockets for the oven, dishwasher and hob ignition (and any other appliances which don't have them).
3. The damaged cable
could be repaired with crimps, but it would be far better to replace the damaged section - particularly as the walls are not tiled/decorated yet, and even crimping will still require that some of the cable is removed from the wall.
4. The socket outlet next to the gas hob needs to be moved further away (at least 300mm)
There may well be other problems not apparent from the photos.
Really, a new circuit should have been installed for the whole kitchen - by the time people have hacked about with what is there, a new circuit would probably be quicker and cheaper anyway.
Work in a kitchen is notifiable, the person/company installing it must either be registered (search for them at
www.competentperson.co.uk ) or have already sent a building notice to your local council.
Either way, the modified circuits must be properly tested before use, and a certificate provided showing these test results.