You could try looking at Chambers and Legal 500, both let you filter firms by practice area and region, so it’s an easy way to see who actually specialises in the areas you’re interested in.
From what you’ve said so far, you might like
Fieldfisher, Kingsley Napley or Irwin Mitchell, but I’m not completely certain as they're different practice areas to what I'm interested in. I think Kennedys also have a strong PI/civil lit department, and you can do a training contract just in medical law there.