Understand it's a British slang phrase and rarely used in other English-speaking countries. When I moved to London, I learned that 'on your tod' meant spending the day alone.
Pro Tip 2/3
Colloquial Use
It's casual and best used in informal situations, not in formal writing or speech. After the party, I found myself on my tod, so I decided to walk home.
Pro Tip 3/3
Feeling Isolated
Can imply loneliness or the fact that someone is doing something without company. She felt a bit on her tod at the new job, since she hadn't made friends yet.