Participants are randomly allocated to one of two treatment groups. In one group, participants are given capsules of simvastatin to take orally (by mouth) for 24 months. In the other group, participants are given placebo (dummy) capsules to take orally for 24 months. At the start of the study, when they receive their medication, participants complete a number of questionnaires and motor (movement) tests (a walking test and a finger tapping test). Participants in both groups also attend a further 6 clinic visits after 1, 6, 12, 18 and 24 and 26 months, where they are asked about their health and any medication they are taking, as well as repeating the questionnaires and motor tests. For 4 of the clinic visits, the participants will be asked to attend in the 'OFF medication' state (having omitted their usual PD medication) so that the researchers can get a true picture of their disease without it being masked by their normal medication.