Unless you have done exceptionally well on LNAT, I think you will be rejcted by King's as you don't meet their minimum critria of A*AA. I was rejected for exactly the same reason for IB qualifications, they asked for 35 points HL7,6,6 and I was only predicted 39 HL,6,6,6. They are just looking for any reason to reject you and reduce their admin workload. It took about 2 weeks from the point of applying before rejection.
I think you'll be concidered at least by your other choices