Essential repairs include smoke emerging from the engine, corroded brake pipes and snapped clutches.
Of the 2,519 complaints to Citizens Advice about used cars in the first two weeks of September, a total of 83% were about faults.
The cases included 139 cars that were only good for the scrapheap.
Citizens Advice said it had helped with more than 84,000 problems with second-hand motors in the last 12 months, making it the most complained-about problem to the organisation's consumer service.
Other common problems experienced by used-car buyers include substandard services, misleading advertising and incorrect information about the car before they bought it.
Citizens Advice added that drivers spent more than £363 million on these dodgy motors.
Of the faults reported in the first two weeks of September, a total of 53% of the cars developed a problem within the first month of purchase and four out of five needed essential repairs.
Citizens Advice chief executive Gillian Guy said: "People are spending, on average, over £5,000 on a second-hand car with many drivers saving for months on end or taking out expensive finance packages in order to afford it.
"With rising day-to-day costs putting extra pressure on already tight finances, people cannot afford for such pricey purchases to go wrong. Not only could it cost families money but it can mean their car is off the road because it is unsafe."
She went on: "The second-hand car industry needs to put the brakes on malfunctioning motors by making sure the cars they sell are in good working order."
Leon Livermore, chief executive of Trading Standards Institute, said: "In this age of austerity, it is important for consumers to have the right knowledge when buying a used car."
Consumer Minister Jo Swinson said: "Last year over seven million used cars were sold in the UK. As Citizens Advice's figures highlight, too many consumers end up footing the bill when their car needs repairs or, worse still, ends up on the scrapheap just weeks after purchase."