Hi Roopa, hope you're OK
Like others have said, why don't you think about other unis? I'm concerned that by putting so much emphasis on *where* you want to a PhD, you're marginalising what it will be like to do the 3-4 years of the subject when you're actually there. You could be missing out on a brilliant opportunity elsewhere by narrowing your choices to Oxford or Cambridge.
If you get a PhD, it will be impressive wherever you get it from (as loing as you don't buy it on t'Internet or anything