Which? said 70% of travel firms are using the numbers, and renewed its call for such companies to be subject to the EU Consumer Rights Directive (CRD) which states that helplines must be charged at no more than the basic rate.
The consumer group found the worst offender was airline Jet2.com, which charges 60p per minute on an 09 premium rate number for its general inquiries helpline.
Airlines including Ryanair, Monarch, FlyBe, KLM, Aer Lingus and Lufthansa also use 0871 numbers for reservations, complaints or other customer inquiries.
Which? also found 15 of the biggest train operators use 0844 or 0845 numbers for their customer helplines.
Which? said it believed consumers should not have to pay a premium to make a complaint, or be faced with a high phone bill if they wanted to speak to a company.
Which? executive director Richard Lloyd said: "Going on holiday is meant to be a pleasure but there is nothing fun about being whacked with a costly call.
"It's a disgrace that people face bumper bills just to ask a question or make a complaint about their travel booking. The Government should close the loophole that allows travel companies to use costly phone numbers without delay."
The investigation found 24 of the 38 airlines included in the study give high rate numbers for consumers to call for customer service or to complain, while 11 ferry companies give 0871, 0872, 0845 or 0843 numbers for customer inquiries.
Coach firms National Express and Eurolines use 0871 numbers for both customer service or complaints, Green Line uses an 0844 number for both, and Megabus has an 0871 number for customer service.
The 0871 numbers in the travel sector typically cost at least 10p per minute to call from a landline, but could be substantially more from a mobile phone, Which? said, while 0844 and 0871 numbers are not included as standard in inclusive call packages from landlines or mobiles.
Which? called on the Government to extend the CRD ban to the travel industry as soon as possible.
Jet2.com said all booking calls would be free from October 20 and customers calling the airline's general inquiries number would be charged at the national rate.
Steve Lee, commercial director of Jet2.com and Jet2holidays, said: "We are in the process of moving our Jet2.com call centre to our headquarters in Leeds from South Africa, so it made sense to review the call charges for our inquiry lines.
"We pride ourselves in providing our customers with the best possible service. Hopefully this move will make it easier for them to pick up the phone and speak to us about their travel and holiday arrangements."