What we do is we try on our own first, maybe ask someone near us for a word or two and then go to our Senior Marker. The SM will sit down with the marker and the script and try to read what they can and then the marker will award a mark. The second marker will do the same thing. If the marks are discrepant then the SM will get to make the final decision.
I have spoken today to the English markers at our school and all of them have said the same thing - no typists at all for illegible work - just no marks or the same process I have described above. None of the markers at my school, and that covers about 70% of the staff, have ever heard of an illegible script being sent for typing.
Yes we do get typed scripts - because the student has some other issue and the special consideration that that student has been awarded includes being able to type their work.