Your description of SA/DA confused me a bit, so I just checked this on my own Webley, with the revolver open:
1) If the hammer is pulled fully back and cocked, the pawl rises up to almost the very end of the slot in the recoil shield.
Please note: this is SINGLE ACTION, i.e. the trigger only releases the hammer.
2) If the hammer is not cocked, but you slowly depress the trigger, the hammer will be forced back and then released. The hammer does not travel as far back as if it were cocked for SA, so the pawl does not rise up so far in the slot. On my revolver, it releases when the pawl is about 1/16" below the top.
Please note: this is DOUBLE ACTION, i.e. the trigger performs two actions - rotating the cylinder and operating the hammer.
I hazard a guess that it is the second case (double action) that is causing you trouble, and the most likely explanation is that the pawl has worn short OR has become very rounded at the tip, so that the cylinder is not rotated far enough for correct DA operation. Check out the 2 points above, and if you see a gap of more than about 1/32" in SA, and much more than about 3/32" in DA, then that would confirm my suspicion.
You probably need a new pawl (heaven knows from where!) or the old pawl needs a rebuilt tip (not a beginner's job).
If, on the other hand, the pawl is long enough, but the hammer is not going back far enough in the SA (hand cocked) position, then maybe someone has fiddled around with the cocking notch. In which case, it is even less of a beginner's job!
Assuming that you are unlikely to find a Webley specialist pistolsmith around the corner, take it to a gunsmith who is familiar with other topbreak revolvers (e.g. S&W). The working principles are similar enough that he will know what to do.