Can anyone give me the link to matings that are not allowed by the KC - know the obvious ones but would like to know them all

https://www.thekennelclub.org.uk/dog-breeding/using-your-dog-at-stud/

Some of this, and the various links, may be of use?  Go to the KC website and you should find what you are after.

Inbreeding - Mother to son, Father to daughter, sibling to sibling although half brother to half sister would be ok .   It's usually helpful to speak with an experienced breeder within your breed.

It's half-sibling mating I was looking at - not very clear on their website - thank you

Been out of breeding for so long that perhaps cannot be very helpful but IMO a half-sibling mating would be subject/acceptable according to the COI  of the half-siblings, and their antecedents. 
Guess I am not explaining this very well but I always tried to keep COI low as a breeder.

It's very basic and easy. No FULL siblings, no mother to son or father to daughter.

> It's usually helpful to speak with an experienced breeder within your breed.

I should have added to do this that if a half brother to half sister is planned by a new breeder, as those within a breed for a long time would know the individuall parents and whether there are any possible problems, with this kind of mating.