These ideas are ways to start thinking about leadership. You’re unlikely to use these as evidence of leadership skills in a written application, but they might be things you reference in conversation at interview.
Suggest activities to do with your group of friends and make it happen. Don’t just be responsive
Read biographies, listen to/watch shows, podcasts, TED Talks etc. featuring leaders you admire
Attend lectures/webinars with people who are leaders in their fields when they visit Oxford – at the Oxford Union, your department, college, societies etc.
There aren't many "short-term" activities that you can do, as most leadership roles require commitment. However here are some quick ways you can start developing leadership skills, that you could refer to in applications.
Organise a team to enter a competition, or a charity run
Become a “parent” for Freshers in your college/department
Organise a holiday for yourself and a group of friends