That's been the case since July last year. If you have both V5's you can send it all off at the same time with you £80 and I think it will only take the week as they are very quick at removing plates from vehicles. The slow part comes when you buy a new car, you need to apply to put the plate on retention, that takes about a week and then wait on the new V5 before you can send off the docs to have the plates changed. That's takes weeks to get the V5 but the changing of plates takes a week at the most.
If you had to do the latter as a two step you have to pay £105, which is a joke because you only have to do that because of the dvla office closures.
I bought my car spur of the moment so hadn't taken the plate off the car........what a right hassle. Got the car 18th January, docs all sent off and got my retention certificate back 28th January, then took until 19 February to get the new cars V5 and then sent that off and the plate was on car 28 February. I already had the plates and checked the DVLA vehicle enquiry to see when the change had taken place so I could get the plate on ASAP. The docs to confirm they had changed the plate arrived over a week later, glad it can now be checked online