You need to do it at the Post Office. Take the Green "New Keeper" section of the V5C "Log book" (you keep this section when the seller sends off the V5C to the DVLA notifying them of change of owner) along with your insurance certificate (which your insurer may email to you, many do now,) and MOT certificate (if vehicle more than 3 years old).
You can't do it online as a) the car probably won't show as insured on the MID, it takes a day (or often more!!) after you take out the new insurance and b) the disc would go to the old keepers address as the DVLA register won't be updated to show you as the new keeper.