It seems that you need to be concerned about more than just the number of hours you work on this machine.
Your employer has a general duty of care under Health and Safety at Work (HASAW) regulations to ensure that the facilities provided for the work you are asked to undertake are suitable and as free from the risk of injury or illness as is practically possible. Since this machine incorporates a display screen it is subject to the Display Screen Equipment (DSE) regulations which are quite specific in terms of working positions, length of time to be used, eyetests, etc. Have a look at this:
http://www.hse.gov.uk/msd/dse/faqs.htm
Measures must be taken by your employer to minimise the risks to you and a risk assessment for the processes you undertake should have been carried out. From what you say none of this seems to have taken place.
You need to have a word with your manager to discuss this. If you get nowhere (as you may well do since your employer seems to have had little regard for you wellbeing so far) you should contact the Environmental Health Department of you local council.