Hi Snowtree,
We had similar problem with my grandmother after she was diagnosed with vascular dementia. By law the dvla mustbe informed about a diagnosis of dementia. Also witholding this information, if an accident occurred, would invalidate the insurance and may result in being fined and losing licence. Information sheet 439 is on this website, entitled dementia and driving, which may be helpful.
We arranged for my grandmother to have a test (organised through an occupational therapist) which she passed. We sent all the information through to the dvla (test write up, letter from GP) who renewed her licence for a year. However she has gone down hill a bit since, so we reported our concerns to the dvla, who sent another medical form to be filled in and stated that if she didn't reply to this within 28 days her licence would be revoked.
Would strongly recommend getting advice from GP or get him/her to write letter to dvla if there are concerns about your dads drving. If you speak to the dvla about your concerns they'll send your dad a medical form to fill in which would have to put down about his dementia and parkinsons.
It might not neccessarily mean he will lose his licence (in my grandmothers case she had a driving test and passed, so licence renewed for a year). Also check to see when his licence expires, dvla will send out renewal forms probably a few months before this date.
Hope this is of help, it is horrible having to do it but it is worth it in the end.
Jodie