No, you don’t necessarily have to be physically present in Oxford or Cambridge for an interview (unless you are applying for a degree such as architecture at Cambridge, which does require students to be present for interviews), but the universities do conduct their interviews with international applicants in slightly different ways.

Oxford gives students the option of either showing up in person or having an interview over Skype, and Cambridge offers in-person interviews either on-site or in a select few locations around the world, so you might be able to have an interview at a point closer to home (e.g. Singapore). If you want to register to be interviewed at an overseas location for Cambridge, you may have to submit your extra paperwork (the COPA and the SAQ - two application forms specific to Cambridge) earlier in the year (20th September) - I suggest you check the deadlines to make sure you’re aware of them early on. If you are applying to Oxford, after you’ve submitted your UCAS application your chosen college will usually get in touch asking if you would like to be interviewed via Skype or in person.