OP has happily said several times that her gross pay for the day was £140. But not the number of hours or the hourly rate paid.
I suspect this is because the agency considers that she worked 6 hours, but she counted 7 hours (8.30-3.30). The reality is that teachers don't get paid for breaks, same as every other employee. And the law says you have to have a minimum of 20 minutes break if you're working a continuous time of 6 hours or more.
So the agency likely paid '6 hours', which is an effective gross rate of £23.33. Even if she worked the statutory bare minimum 20 minute break, the hourly rate would be at least £21.02. But an hourly rate 31%+ higher than the take home number OP is all outraged about doesn't fit the narrative, so all posts for 40 pages pointing this out have been conveniently overlooked.
For a full time teacher with PPA load, 10 hours a day for 195 days at the £23.33 rate would be a salary equivalent of £45,500.
So we're all agreed that the OP is either grousing about not getting the additional PPA work hours to do when working supply, or objecting to the tax deduction. I'm sure the £112 net from £140 gross is correct, as for 1 day a week, she won't cross the minimum earnings thread for NIC & pension in her second job. But will pay tax at a straight rate of 20% because her tax free allowance is applied in full to her first job.
This is probably why the net pay looks a pittance compared to her salaried 50% time job, because she is effectively paid for 10 hours a day (195 days a year) in that role, not 6, and only has an effective tax rate of around 12% on those earnings.
But using the gross hourly rate to compare to receptionists, wait staff & cleaners is far too much like inconvenient logic, so here we are.
Hope OP got something out of all of this, in the end?!?