Is the Ilex General a dial set shutter? SK Grimes warns they were the only real dog shutter Ilex made and cannot be made reliable:
http://www.skgrimes.com/ilex/index.htm
If it's working at all, It's apparently in better shape than most. Besides, if T and B work OK, and the top instantaneous speed works OK, it can still be fairly useful.
I bought an old rapid rectilinear that some previous owner had removed the air brake cylinder and the linkage from that cylinder to the shutter speed dial. This was probably done because all the slower speeds were completely unreliable. After a little careful cleaning and TLC, I got T, B and 1/100 to work fairly well. It fires at 1/100 (probably more like 1/50) at all marked speeds except B and T.
With a little practice, you can use B with fair accuracy down to 1/2 or even 1/5 second by carefully practicing alongside another shutter of known accuracy. If you need 1/10 and 1/25 is your slowest speed that's reliable, fire the shutter at 1/25 two or three times.
That trick only works if your subject is holding still, but it was devised by owners of box cameras with one fixed instantaneous shutter speed.
All is not lost. I think you'll like the lens, if not the shutter.