The seller will need to do the transfer or at the least either transfer/retain it.

Once that's done and they have allocated a new reg number to the vehicle, DVLA then send the log book off to them.

The seller then does the log book in the normal way to new owner (matt), with the new reg number and then send it off for your details to go on it.

If as the OP states and wants the log book ASAP, then that won't happen and could take a fair few weeks to come back in his name....