While there aren't any official published breakdowns of A-Level results each year, Ali1302 on The Student Room worked out the following stats based on figures for the 2012 results:
% achieving AAA or above: 12.92%
% achieving A*AA or above: 9.21%
% achieving A*A*A or above: 4.95%
% achieving A*A*A* or above: 2.14%
Since you're asking about medicine though, Critical Thinking and General Studies wouldn't be considered in an applicant's results. These are the percentages excluding CT and GS:
% achieving AAA or above: 12.53%
% achieving A*AA or above: 8.92%
% achieving A*A*A or above: 4.77%
% achieving A*A*A* or above: 2.03%
Because of the way that grade boundaries are calculated, the number of people getting each grade is usually about the same year by year so although these figures are a few years old, they should still be in the right ballpark.
So based on these numbers, the top 4.77% of students achieve a combination of at least A*A*A.
Owen Haigh, MBBS Medicine, Newcastle University (2023)
Source: Quora Digest