The Driver and Vehicle Standards Agency (DVSA) has confirmed the Bede Industrial Estate centre is being “evaluated”.
Full details are yet to be announced, but closing the South Tyneside test centre would see their operations moved Sunderland.
An online petition opposing this has already attracted over 2,000 signatures. Campaigners say South Tyneside learners would need to travel to Sunderland for lessons, as they would eventually have to sit their tests there.
They say this in turn will lead to longer waiting times for lessons and tests, increased lesson costs, learners used unqualified instructors such as parents, possible loss of skilled instructors and examiners, more pollution due to extra commuting and more congestion in Sunderland.
In November Jarrow MP Kate Osborne wrote to the DVSA and Mr Schapps, setting out her opposition.
Now council leader Tracey Dixon has also contacted the minister.
Cllr Dixon wrote: “The proposal to move tests to Sunderland would mean increased lesson costs and delays for South Tyneside learner drivers.
“The extra time and costs will not just make it harder and less appealing for most people to get a driving licence; but they will indirectly also have a detrimental effect wider career and financial prospects, insofar as they will make it harder for people to access jobs further afield for which a driving licence is a prerequisite.
“The South Tyneside Driving Test Centre is a key asset for enabling local people to improve their options and its loss would be sorely felt among the local community.
“I urge you and the DVSA to urgently reconsider this ill-thought-out plan.”
In a letter to campaigners last month, DVSA chief executive, Loveday Ryder, said: “A larger site in Sunderland is approximately 5/6 miles away and the examiners at South Shields will be working at Sunderland to ensure our local service delivery continues to maintain a high standard.”
A DVSA spokesperson also said: “We have carried out a review to ensure that service provided locally continues to be of a high standard, and the impact of any proposed closure is minimalised.”