It is possible to find a balance of structure without too much stiffness! It does take some looking, however, and unfortunately, since I'm in the states I'm not much help when it comes to where you might find one. However, maybe my experience with my current clutches can help.
My teal snake Kate Spade clutch from Una is the stiffest one I own, and it is hard to get all my usual stuff in it, but if I leave out my eyeglass case, for example, it works fine (this works for me because most days I'm also carrying my tote with papers, iPad, lunch, etc.).
However, I have a large raspberry envelope style clutch from Foley & Corinna that holds everything beautifully despite the leather being soft. I think it's mainly because the bottom is gusseted -- it will even stand upright. This might be something to look for. I got mine on one of those flash sale sites -- Gilt, I think. It actually came with a chain strap, which I promptly removed.
My other clutch is by Melie Bianco, and I found it in a local boutique -- it's envelope style and no gusset (but also has a removable strap), but the leather is just soft enough to accommodate stuff without being floppy. Maybe a search of the name will unearth something near you?