10 weeks is entirely possible. I passed in just over 3 months and many have done it in a shorter time than that.
I did a 2 hour lesson once a week, although this increased a little bit as I neared the test. It will ultimately depend on the ability of your instructor as well as your availability and ability to learn. Look for reviews off friends for instructors in your area, but also check out their background - An ADI Level 6 instructor is the highest standard they can have.
I didn't book my theory test immediately after turning 17, but it can take a few weeks and this will ultimately dictate when you can go on to do the test, so don't leave it too late. I'd leave it a couple of weeks before booking just so that you can get used to driving a little bit and it may give you a little more perspective when answering the questions. It's entirely possible to fail the theory test because of the idiotic system they use to test you (hazard perception, which has little or no relevance to actual driving ability) so leave enough time in case you do have to do it again. I narrowly passed, but it's an awful test.
If you can drive another car whilst taking lessons (such as a parent's car with provisional insurance) then you may be able to learn faster, although I don't really trust the ability of parents or friends to instruct someone how to drive.