Barrister is a terrible profession unless you have family in it or come from an extremely wealthy family. You make no money for at least the first ten years - to the extent a large number of barristers also work as waiters etc in the early days. Please look up salary/poverty issues for young barristers. Most leave the profession after 5 to 6 years.

Also yes, a law degree will make the process much easier. If you actually want to do law, then do law. If you're on the fence with law, pick a degree that will lead you to wider career options. Classics, to be frank, is about as limiting a degree as you could choose. Potentially look at doing politics and economics, something that is slightly more applicable to the real world and you might be able to do a few law modules. Wanting to be a barrister but not enough to commit to a law degree says to me you're not actually interested in law, you're interested in the pageantry of law and law tv shows. The latter is fine, court is pretty cool, but be very sure you're also interested in law itself.