How and when to stop working is one of the most important decisions that anyone diagnosed with Parkinsons while employed has to make. I recently made that decision to stop based on the fact of how I felt, both physically and mentally, my financial situation and from taking the advice of others. Although I am physically probably quite capable of doing some work, mentally I am totally exhausted and if I was quite honest I would be a liability for any employer. My last day of work is at the end of March and both my employer and I have come to an agreement where upon I will leave on grounds of capability due to my ill health. I'm sure everyone is different and every employer might take a different stance on the situation (not withstanding any legal obligations that your employer has).
The advice that I would give is if you feel that your quality of life would improve if you were not working, if the sums add up (benefits+pension+savings+other income) and if you have the support of others then go for it. If you feel that you can't go on any longer then don't hesitate, see your doctor and go sick, SSP and ESA should soon follow. If you are off on long term sick a situation would eventually be reached where they could dismiss you on grounds of capability. However, to avoid this long drawn out process your employer might be willing to come to some compromise agreement with you where you could leave sooner provided that this did not put you at a disadvantage financially. Seek professional advice on this, if you are in the Union that's a good start.
Finally, as Gus says, don't hesitate to call your local support worker, I have found them caring, supportive and can put you in touch with the right people if you need specialist advice, especially in regards of getting the benefits that you are entitled.
Hope some of the above helps and good luck