I can't tell you about how quick you can finish an EPQ, but I can tell you that it'll hardly make a large impact towards your Oxbridge medicine application. They don't value the EPQ necessarily more than (maybe not even the equivalent of) other aspects in your application. Frankly the major concern I see is, if you're doing it then you'll likely want to make it good, but if you're rushing into it then it'll be difficult to achieve that. I've seen and helped friends with their EPQs and it definitely took a substantial chunk of their time but they planned ahead. Personally I think your time would be better allocated towards perfecting other parts of you application (that's what I did) and it'll more likely give you an edge in applying than doing an EPQ. Hope that helps!