What the guy told you is correct. You need to have someone (a qualified professional -- doctor, shop owner, vicar, teacher, etc.) who has known you for two years sign the back of your photo. Since you haven't been here two years, you can take your photo to the DVLA to have them verify it. UK passport holders can have their passports verfied at a Post Office offering the service, but we have to send our passports to Swansea.
Not sure about the timing, though. You might have it back much sooner than 6 weeks....they probably just say that to cover all bases.