My view on your questions:
Some firms, eg McKinsey, bring doctors and PhDs at post-MBA level, so theoretically you could enter at that point. However, with just two years of experience, I would be very surprised (actually astonished) to see that happen - it is just not really feasible to expect a 25 year old with no business experience and very limited medical experience to work at that level.
Therefore, at the moment I think the two options are :
1) They bring you in at entry level - but you have just missed the whole recruiting cycle.
2)They bring you in at a slightly higher level, but unless they have a specific need for a doctor, why should they do that in the current environment?
In any case HR will bring you in at the appropriate level. I think getting in will be the bigger problem than the level of entry right now.
Wrt your CV, I would get some people working in consulting to look at it and advise you. Most medical CVs I see are totally inappropriate to consulting and wouldn't get through the HR screen so you really need to work on this. You have about one A4 page to highlight academic excellence, rapid career progression, impact at work and in the rest of your life, teamwork and leadership, and also sound interesting at the same time. It will be difficult with just two years - up to you to work out how to do it. If you can't then you won't get through the CV screen as plenty of others can.
In terms of timing, I am afraid you couldn't really pick a worse time. I know for a fact that a few doctors have recently joined consulting firms in London and many more have applied unsuccessfully. There is only a finite need for doctors, and if firms have enough it doesn't really matter how good you are, you won't get through. We are also in the biggest economic downturn for decades and people are being laid off rather than hired.
Having said that, if you don't apply then your chances are 0%.
Sorry this post is rather negative, but that is how I am seeing things right now. In order to add something constructive I would suggest:
Apply as soon as you feel you are ready, as you have nothing to lose from doing so
Have plans B and C to fallback on if it doesn't work out (and to be honest that is the most likely outcome right now).
So in summary, if I was in your shoes:
Plan A - apply to everyone, but don't have too high an expectation of anything coming from it.
Plans B - Apply for medical advisor roles in big pharma (when you have another year of clinical medicine under your belt, and preferably an exam). This will add more relevant business experience to your CV that looking down ears and writing TTOs won't.
Planc C - MBA after another couple of years in medicine. Only go to full-time programmes in top schools. This will demonstrate the commitment that firms want to see, and also provide you with some business knowledge/skills and a network.
I am afraid my answer is rather more negative than the previous posters, but that is the way I see things now. As I said, you have no chance if you don't apply, but I do also think you will stand a much better chance with more experience or a few more strings to your bow alongside just two years of medicine (ie MRCS, pharma experience, MBA etc etc).
Bear in mind that, at the moment, employing you is a big risk for firms that are desperately trying to minimise risk.
Good luck with it