In reply to DVH:
The area most remote from a roadside in the UK is at the headwaters of the River Feshie and the watershed area from the River Geldie. Nearest roads are at Achlean in Glen Feshie and Linn of Dee many miles and hours walk away. Unfortunately for solitude-lovers, this area is also crossed by well-used tracks crossing from Glen Tilt to Glen Dee, Glen Feshie and the Lairig Ghru; the Tarf bothy is also not too far away.
About ten years ago I backpacked from Tarbert in Harris through to Timsgarry in Lewis. I stopped at the old abandoned hamlet of Kinloch Reasort on the way and sheltered in the lee of one of the derelict buildings. Presently, across the river, in one of the buildings still looking robust, I saw a figure leave the house, cross the river and walk up toward me before sitting down to chat. I could see he was an estate worker or gamekeeper, so after a while I asked him if he was checking me out to see if I was carrying illicit fishing rods or poaching gear. "Oh no," he replied, "I just haven't seen anyone for nearly a week, so wanted a chat."
The other obvious answer to the question is St Kilda. Though again, finding solitude even here will be difficult, at least during the summer. Perhaps less so on Boreray or Soay.
Post edited at 10:51