2 seperate transactions.
£80 to remove your plate and that plate goes on retention for 10 years (£25 a year renention fee has now gone), they issue a replacemnt plate and then after you've got all that you can put your new cherished plate on, another £80. Or at least that's what I did for my father's car a few months back when swapping his cherished plates over.......complete faff and a money making scam IMHO.
Yes, it will require two steps, and two £80 payments.
It has improved with the £25 fee now disappearing, as above, and you can do the retention / transfer online now in seconds, once you have a log book in your name. Sequential process....pay £80 to take the old number off, and replacement log book and retention certificate will arrive within a week; then with the new retention certificate for the new number, do it online =another £80 fee; and another new log book.
Remember to inform insurance too as soon as it's done (and pay their admin fee - circa £20). You may get away with one fee for the insurers if you tell then what you are planning to do, or if your insurance renewal is due soon, you might want to wait and do it at renewal within the admin period, and no fee should be charged then (cos they want your continued business).
Another tip, if you keep your old plates, the DVLA usually put the car back on its original registration number if you ever take off the new registration/s - save you buying more number plates from Halfords, or wherever.
With the old, pre-online service, it would have taken months to do this, so the new online way is much better, but still money for old rope!