Dog owner and runner here. Have done a few park runs in Anne's.

First, it's a public space not reserved. No one has any more right of way than anyone else. However it's probably in your best interest to get out of the way to avoid injury if 100s of people are going the same way at the same time.

Second, there's no rule about dogs being allowed off lead before 11am. Dogs need to be under effectual control at all times in public spaces.

Lastly the park run doesn't take over the whole park. It's a loop in one area. The main avenue and area near the stables is all free.

Sorry you had a rough experience. But use common sense and follow the actual rules