I actually wasn't a member of TSR, didn't even know it existed, until a friend of mine showed me this thread, and I joined specifically to reply to your questions. Without knowing anything about you, except for what I can glean from your other posts on the forum (apologies for the stalking), it seems you're in pretty much the same position I was in five years ago, and perhaps my experiences can shed some light.
For background, I attended a London public school, left in '04 with exactly the same GCSE grades as you and 5 A Levels at Grade A, not including General Studies, including Ancient Greek. Didn't do Latin to A2. Went up to Oxford to do Classics, graduated summer '08, currently have a job in London at a City law firm.
Your comment about being surprised at how difficult it was to get a job flagged my attention. Recession notwithstanding, and the recession will have passed by the time you graduate anyway, it is increasingly becoming true that DOING A CLASSICS DEGREE WILL MAKE YOU PUNCH BELOW YOUR WEIGHT ON THE JOB MARKET. End of story, anything anybody else says is crap.
Of the 16 Classicists who graduated from my college while I was at Oxford (4 in each year over 4 years), I was the only one to leave with any sort of job in hand, and that is not for want of trying on the part of the others. I didn't know all the Classicists in my year across all the colleges, but I knew many, and I can count the number of people who graduated with decent jobs in pocket on both hands. Some wanted to study further, fine, but a disproportionately large number applied for high-flying jobs and didn't get them.
Without wishing to be disparaging, but feeling a duty to tell the truth plainly, if you are going to be happy looking for a rubbish job on Craigslist (or whatever) when you graduate, then do Classics. But if you're bright and ambitious, and think that with an Oxbridge degree you should probably be looking for a high-flying job (City, big-law, government, &c) upon graduating, then you will be making life much harder for yourself by doing a Classics degree. Do PPE, go to the US. Don't do Classics.
If you're interested, I think there are a number of reasons for this. Firstly, at entry level, I think Classics has stopped attracting the bright, motivated and ambitious people it used to, these have all defected to PPE, Law, and other such degrees. Secondly, let's not beat about the bush, Classics is a degree respected only within a small and priviliged circle (it has little cachet to people who aren't white, who aren't English, who didn't go to certain schools). Globalisation has taken hold, and the people who interview you, the people you will have to work with in the future, might well not be part of that circle (look at the big City banks in London - how many of them are foreign owned, and staffed with global people?). This is NOT a globally respected degree - it is a victim of globalisation.
My advice to you: don't lay down in front of the train. If you're bright enough, which you may well be, you'll might do fine (I did). But you might not, and that's not a gamble I could, in good faith, urge you to take.
If you want to go to Oxford, do PPE, it's a much better degree in terms of the material you will study anyway, more interesting, more relevant, more useful to you if you want to go on and do big things later on in life. Oxford is a good place to study Classics, which in itself is a fulfilling and stimulating degree, but there is a significant opportunity-cost, which I think you should only take if you're really interested in the subjects, at the expense of all else. Since you only studied Latin and Greek to GCSE, it seems to me that you might not be.
For the third time: do PPE, or go to the US, where you can study a breadth of subjects with similarly intelligent, motivated, and globally-minded people.
Sidebar: Regardless of what you might read in the criminally-misleading prospectus documents which the Classics Faculty publishes every year, you absolutely won't get into one of the academically-stronger colleges to study Classics without having Latin and Greek to A-Level/IB Level. People do get in to Oxford to study Classics II (without the languages at school), but everybody who I know who studied Classics II was relegated to a fringe college - not the one they applied to - with lower academic standards. Not a huge problem, Oxford is Oxford, and any difference is pretty small, but perhaps a relevant consideration nontheless. (Seriously, somebody should sue the Faculty for the lies they publish in their marketing documents.)
Jammy, I won't be checking this site too often, but do message me if you want to discuss this, or other issues, further. Best of luck to you, and to all, in your applications.