I submitted my application to DVLA back in October (cheque dated 31.10.16) cheque cashed the next working day, between Christmas and new year they asked for more information? so I sent photos of bike, engine and frame number etc, last week I phoned DVLA and they said they would write to me in the next two weeks!!
Twenty weeks now!!
If I put the reg number into the DVLA system it comes up strait away, so I do not know what the delay is.
Good luck with your application but don't expect DVLA to be quick.