The warning from the DSA comes after more than 123 people have been arrested for offences relating to illegal driving instruction in the last four years.
Of those 39 were convicted and 31 received police cautions, the DSA said.
Police have warned getting into a car with an unlicensed instructor who has not undergone the obligatory criminal background check is as dangerous as getting into an unlicensed minicab.
Inspector Vince Brady, of the Met roads unit, told the BBC: "We talk an awful lot with people around using a licensed minicab, because you've got confidence that that vehicle, that person, is subject to a process and a series of checks.
"It's exactly the same with learner drivers. They're getting into a vehicle with a stranger they may know nothing about."
Learner drivers also risk missing out on key driving skills essential to instructors being awarded a licence.
DSA's Head of Fraud and Integrity, Andy Rice, said: "We urge all learners to ensure their instructor is qualified to teach by checking they display a valid DSA badge in their windscreen. Learners can also use the free 'Find a driving instructor' service on GOV.UK to see details of their nearest instructors who are approved and registered with the Driving Standards Agency.
"All approved driving instructors undergo regular assessments of their ability to teach and are also CRB checked.
"Illegal driving instruction is rare but when it happens it can potentially be very serious. We investigate all reported cases and work with the police to bring offenders to justice."