The supposed incident happened on Monday night around 4am, when two friends were driven from Wrexham to the Ceiriog Valley.
The women claim that they were forced to pay or be driven back to Wrexham.
However, Wrexham and Prestige Taxis denied that the car was locked and said that the women showed “classic signs of doing a runner”.
Jools Payne, one of the women’s mothers, said her 21 year old daughter and her friend ordered a cab after a night out, from the town centre to drive them back home.
Payne claims that the women agreed an £18 fare with a taxi marshal and were by “no means wasted”.
The women were told the fare had risen to £26, one mile from the destination. Which is when the taxi driver supposedly locked the car doors, then told the passengers that they would have to leave a mobile phone while one of them went to get the cash.
Payne says that the women were threatened to be driven back to Wrexham but they agreed to pay the extra charge.
While the cabby had her daughter locked in the taxi while her friend went to get more money, she claims that the driver was in a “temper”.
Payne said, “My daughter tried to get out of the taxi but both the back doors were locked. At this point she felt very vulnerable and slightly panicky.”
The cab driver also demanded an extra £10 for “wasted” time, which the women refused to pay, said Payne.
She said, “My daughter, by now feeling quite fearful, kept trying the doors, but they remained locked whilst her friend was in her house getting the extra cash.
“The additional fare was given to the driver but the pair bravely refused to pay the further £10 he had demanded for ‘wasted time’ and he finally released the door locks.
“My daughter got out of the car and he simply sped off.
“The girls were left shaken by the experience at the time but today that has given way to anger and dismay at their treatment by the taxi driver.”
She added: “As a mother I am alarmed and appalled at this man’s behaviour.
“We worry about our youngsters when they’re out partying but we expect them to be safe in a taxi.
“To my mind, locking a young woman in a car and refusing to let her out is tantamount to withholding someone against their will.”
Wrexham council has received a complaint and will look into the matter. North Wales Police also confirmed that they had received a complaint and will be investigating.
Wrexham and Prestige Taxis spokeswomen said that the driver was an “excellent” employee with commercial taxi insurance and has been working for them for 3 years.
The spokeswoman said that CCTV which was installed in the vehicle would be reviewed and also said that the car doors were never locked.
The driver had overheard the women saying they only had £12 between them and were texting each other to plan “a runner”, the spokeswoman said.
She said, “He told me he was going to drive them back to Wrexham and take them to the police station because they obviously didn’t have enough money on them.
“They wouldn’t give him an exact address either. These are all classic signs of doing a runner.
“He’s done nothing wrong. In all fairness, I think he’s done everything fine.”
The spokeswomen also said that the women had specified Chirk, which is why they were originally quoted £18, but the journey was to the Glyn Ceiriog Valley.