Published Wednesday, 13 August 2014
It comes after DVA centres in NI closed in July as part of a move to centralise services in Wales.
A number of local people who now have to use an online service to tax their car have reported having problems with the system, while some car dealers have also experienced difficulties.
Mr Durkan, of the SDLP, has written to UK Minister for Transport Robert Goodwill to highlight his concerns and to call for Swansea to "up its game".
He said: "The public and the motor trade have raised concerns such as the time taken to get vehicles registered or taxed and also the difference in MOT testing periods between NI and GB.
"I am very disappointed and concerned about ongoing problems that people are facing.
These concerns have been raised with Swansea and an immediate response requested for the customers involved.
Mark H Durkan
"I have written to the Minister for Transport to highlight these problems and to make it clear in no uncertain terms that Swansea needs to up its game."
Customers in Northern Ireland have the option to use an online system or the post office to tax their cars following the closure of the eight local DVA centres earlier this year.
However some users have experienced difficulties with the online process.
Bill Megraw, who has two cars to tax on the new online system, said: "One of the problems was the when you go on to the screen it tells you to enter a sixteen digit reference number of the letter that you've been sent telling you that the tax is due. There isn't a 16 digit reference number.
"The Northern Ireland letter seemed to come out with 24 digits."
Meanwhile car dealers said they have also had trouble because in England, a car must get an MOT test after three years whereas the test in Northern Ireland is carried out after four years.
This has resulted in some dealers having their application for car tax rejected because the vehicle they have bought over from England doesn't have a valid MOT in NI.
Local dealers said this is impacting upon their sales.
Whenever it first happened we spoke to Swansea and the people we were speaking to initially didn't even realise that we had different number plates in Northern Ireland.
William McCausland, car dealer
In a statement, the DVLA said the majority of NI records were successfully merged but recognised that there have been "some technical difficulties for a small number of vehicle records".
A spokeswoman apologised and said they are working to resolve the problems.
"The recent changes to vehicle registration and licensing services in NI have been delivered in full consultation with the Driver and Vehicle Agency and stakeholders in NI," she said.
"We worked closely to address any anomalies identified between the two systems and as a result, the majority of NI records were successfully merged with DVLA's on 21 July.
"However, there have been some technical difficulties for a small number of vehicle records that have migrated from NI, which has resulted in a small number of customers having difficulty taxing their vehicle, particularly if they have recently changed their registration number. We are working to resolve this issue quickly for our customers and apologise for any inconvenience caused."
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