The Driver and Vehicle Licensing Agency has been described as a "shambles" in its handling of car registrations.
Delays in the process are causing car dealers large amounts in disrupted cash flow, according to the Scottish Motor Trade Association (SMTA).
It said jobs will have to go unless the delays are resolved at the Swansea office of the DVLA.
Swansea is now handling 20,000 of the applications each week, following the centralisation of work.
The DVLA has started to wind down its network of regional offices.
Since July, applications to transfer a personal registration plate from one car to another have had to go to the Swansea headquarters, and have taken longer than the guideline seven days.
Douglas Robertson, chief executive of the SMTA, said it can take up to six weeks, though the DVLA says it delays are closer to two days over the deadline it sets itself.
It has, however, apologised to car dealerships.
"We would describe it as a shambles," said Mr Robertson. "Centralisation is intended to save the UK taxpayers a considerable amount of money in the future but the current cost to UK businesses and taxpayers could well exceed any savings.
"This is causing frustration among consumers who cannot put their cars on the road until the transfer is complete, and also to many of our dealers whose cash flow can suffer badly whilst waiting on the numbers to be received.
"Being over a million pounds out of pocket for a few weeks can cause great difficulties for a retail business in the motor trade and we believe it is only a matter of time before jobs are lost.
"This will have been caused by the incompetence of a UK Government Agency funded by the taxpayers."
A DVLA spokesman responded: "The maximum processing time for personalised registration applications has not changed with the introduction of the new process, and we are still committed to our turnaround time of seven working days from receipt of the application at DVLA.
"However, we are currently experiencing some delays in the processing of personalised registration applications which means some applications are delayed by a couple of days. We are working to resolve this and expect to be back within usual processing times shortly.
"We remain committed to delivering the best service we can. Our continued movement towards digital transactions and the greater use of other organisations to deliver services on our behalf will make it easier for customers to deal with us in a way that suits them."
In a separate statement sent to dealerships earlier this month through the Retail Motor Industry Federation in London, a DVLA spokesman said: "The DVLA apologise for inconvenience caused and thank you for your patience at this time of local office transitions."