The Scottish Motor Trade Association (SMTA) has singled out the Driver and Vehicle Licensing Agency (DVLA) for its handling of applications when people buy new or second-hand cars and wish to assign a vanity number from another vehicle.
It accuses the Swansea-based Government agency of incompetence over the situation and says delays in assigning the numbers are costing the industry dear.
Dealers say their cash flow is being badly disrupted as people wait for personalised plates to be processed. In previous years this would normally take up to eight days, but the SMTA says cutbacks to DVLA staff have caused the procedure to grind to a halt for weeks at a time.
It claims the delay means cars are not changing hands and some car sellers are being left out of pocket by more than £1 million while transactions remain on hold.
Douglas Robertson, chief executive of the SMTA, said he believed it was "only a matter of time" before jobs were lost and businesses were forced to close. He said: "The DVLA is centralising its processes in Swansea and intends to close all its Local Vehicle Licensing offices.
"Centralisation is intended to save the UK taxpayers a considerable amount of money, but the current cost to UK businesses and taxpayers could well exceed any savings.
"Being more than £1m out of pocket for a few weeks can cause great difficulties for a retail business in the motor trade. We believe it is only a matter of time before jobs are lost, and this will have been caused by the incompetence of a UK Government agency funded by the taxpayers."
Mr Robertson said he had contacted Scottish Secretary Michael Moore with his complaints and said some SMTA members had been given misleading information by the licensing agency.
He said: "It would appear little or nothing is being done about this disgraceful situation and we believe it essential consumers understand the delays are being caused by the incompetence of the DVLA, not their local dealer."
The personalised registration industry has turned into a multi-million-pound business since it took off in the early 1980s.
Millions of rare and unusual combinations of numbers and letters flood on to the market all the time for drivers who wish to identify themselves, relatives, business or personal interests by the vehicles they drive.
Since 1983, the agency has kept back some combinations of numbers and letters which it thinks are attractive to people who wish to have their name or initials on their vehicle.
These are marketed separately at a premium through special sales, with some of the most exclusive costing thousands of pounds. It does not include countless others on the private market.
The most coveted plates are those issued to new vehicles before February 1963, when there were so few on the road that they consisted of up to four number or three letters or vice versa.
The most expensive registration plate in the UK is F1, bought for £440,000 by a businessman in 2008.
A DVLA spokesman said the agency remained committed to meeting its seven-day turnaround targets, but added: "We are 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."