One of my recent find of independent designer is Ling Wu. I have not bought any bags from her. Her designs are okay, imho. I do like the softness of the leather. The prices are still steep for the average customers. Her website: http://lingwu.sg/.
I trust my instincts and don't always go for mainstream, however I do like to know there is a stability about a brand in case I need some good old fashioned aftercare. If I was spending a lot of money I probably wouldn't spend it with someone like L'Wren Scott or The Row although they appear fabulous. I prefer leather goods makers rather than fashion designers. Some of the following I don't actually own but I have had the pleasure of viewing, I would have no problem putting my money where my mouth is though .
Perrin Paris, modern in an old-school way
Launer London, very old-school, although for me to buy a bag they would have to make them a bit bigger.
Tanner Krolle, London. So under rated, great history and styling.
Quentine Mackay, a wonderful designer.
Delvaux, I think it's still Indenpendent.
Chanel is still independent and I do like an occasional Chanel bag .
House of Florence, run by the real Gucci family. If I lived in Italy I would be BROKE!.
JT Bags, stylish and quality.
Richard Emden, made in Thailand but very well.
Libertys, well I LOVE mine (3)
Bracher and Emden, a totally different style statement but unmistakable
Sonia Rykiel, again a little bit of something different.