Following a FOI request made by Mr K Johnson, King's College London has published its admissions statistics.
Medicine is the most competitive course at KCL with an offer rate of just 2%. If medicine was excluded, the offer rate and acceptance rate for 2012/3 would be 37.8% and 17.8% respectively. In 2013/4, it would be 40.9% (offer rate) and 18.3% (acceptance rate) and in 2014/5, it would be 44.0% (offer rate) and 19.9% (acceptance rate).
The source for the original FOI request is linked here.