I'm a 3rd year Medic at St Andrews.
Yes, its true that you can make an independent application. This year I know of one person who got into Cambridge out of several around 5 who applied. They require a 1st class honours 17+ in every semester of years 1 and 2. After that your acceptance depends on how well you do at interview and your extra-curriculars.
Last year one person also went to Cambridge.
There have been people who've gotten into King's College London and a few who've gone to Bart's recently I believe, which is a new partnership that St Andrews has developed in England.
Regarding the "guaranteed" routes:
The vast majority of people will go to either Manchester, Edinburgh, Glasgow, Dundee, Aberdeen or Barts.
As of now all Home students are put into either England or Scotland. If they are on the Scotland route they will get to go to either Edinburgh, Glasgow, Dundee or Aberdeen. If they are on the England route they will go to either Manchester or Barts.
In the Manchester route the students are split into 4 base hospitals: MRI, Wythenshawe, Salford and Preston
International students seem to all go to Manchester, and Canadian students to Edinburgh.
From what I know most people on the Scotland route get their first choice offer, with the exception of those wanting Edinburgh.
Manchester seems to be pretty similar although I've heard that MRI may be more popular, but it is more or less well established that Preston is the least popular due to its more remote location.