You can use a layered option. Frosted acrylic or polycarbonate tends to be expensive, so you can get a thin sheet of that, maybe 1/4" or 1/8", then get a clear support piece the same size but thicker as your base. You don't need to glue them together, or anything, just lay the frosted piece over the clear. In fact, I've done a fair bit of gluing/cementing plastics together on their large faces. It's really difficult to avoid bubbles even with small faces of less than 6", especially when using a solvent based cement, since you only have a short time to remove the bubbles, so I'd suggest against gluing them together.
Side note, acrylic will scratch more easily than polycarb, so I'd suggest getting the top piece as polycarb, even if you use acrylic as the support material. Heck, you could use a piece of glass as support, but then you still risk breakage.
You would also want to make sure you are supporting the full perimeter of the frame. Plastics tend to be less rigid than glass, but that's also what helps prevent plastics from breaking.
With plastics, you can also drill holes through the sheets and use screws or bolts to try to put tension into the sheet to help prevent sag by attempting to stretch the sheet. That's not easy, and I haven't tried it, and doing it too much could cause the holes to crack. It could also cause stress interference in the sheet or cause the sheet to warp. It might not be worth this approach, now that I think about it. But having the sheets held down tightly and more than just sitting there will help prevent sag.
I'm from the US, so getting a piece of acrylic or polycarb larger than 4'x8' (1.2192m x 2.4384m) would be a special order. I'm assuming you already have a supplier that can go that large? If you haven't, I found at least one by searching "acrylic sheet sizes uk", or whatever country you are from.