Dead easy and it 'll cost £80. get the forms form the Post office and take to your nearest DVLA office. they'll do the doings and then you can change the plates on the car. Remember that you can't legally sell the old car until you've had the registration document through from the DVLA- if you do the new owner could claim the reg no.
Get it done now and you won't have this problem- when I changed cars I had my old car sitting for a month waiting for the paperwork to come through