Edinburgh I'd avoid if you haven't got all A's at AS level.
But for most med schools, you just need AAA predictions and at least a B in the fourth AS you drop.
A medical school application also includes GCSEs, personal statement (voluntary work, work exp, extracurriculars, motivation, insight into medicine), admissions exam (UKCAT/BMAT but not for Liverpool, B'ham, Bristol, Lancaster), reference, and interview.