The best thing you could do would be some sort of summer school or any educational programme, however, these are very competitive and often are very hard to get into, many may not even go ahead with coronavirus.
One easier way to improve your chances would be through reading books and listening to podcasts, whilst doing school work or other activities you could listen to podcasts, which make it an efficient strategy to boost your application.
Some schools offer the chance to take the U.K. Senior Maths Challenge, which is a test that is used to find candidates for the maths olympiads, but any participant can receive an award (Bronze, Silver, Gold or Kangaroo), which show ability in more theoretical maths questions, and would be closer to tests you would likely receive in an interview. However, this test is conducted in early November, so if you are intending on applying for Oxford or Cambridge, this may not be plausible. Many schools offer this, but you can also enter privately (I expect) and it could increase your chances.
Another good thing to put on your application is any semi-relevant work experience, if you could, contact an accountancy or engineering firm for even a days work experience, these show some commitment and it would be difficult to find any work experience in an entirely mathematical field.
One thing I personally did (although I applied for economics) was to help out in lessons of younger students in your school, if you are a private candidate or at a college, this may not be possible. These lessons can show you’re keen for maths, and even if they don’t, they can show that you are helpful to younger students.
Obviously you would not need to try all of these, but any of these should be able to boost your chances along with the suggestions from previous comments.
Hope this helps!