Danny Cox, the head of communications for Hargreaves Lansdown, said that a number of factors had led to a fall in brokerage fees, which could continue.
"Stockbroking fees have come down in price significantly in the last 20 years as technology improvements and scale have reduced transaction costs," he told CNBC via email. "Over time you would expect that further technology and scale improvements would see stockbroking and investment fund management fees decline."
Buying U.K stocks through Degiro costs around £2 ($3.10) and there's also no fee for opening an account. Other low-cost brokerages include X-O, an online share dealing company, which charges a flat fee of £5.95, and U.S.-based Scottrade, which charges $7 for online trades.
U.K.-based Hargreaves Lansdown, meanwhile, charges as low as £5.95 ($9.22) on some trades, and no more than £11.95 for online trades. It also has no account setup fee.
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Degiro's Nagel said that rather than relying on fees for revenue, brokerage firms will turn to advertising, as well as selling their software to other companies and charging for proper asset management.
"Trading will be free," Nagel said. His company, which launched in the U.K. last week, said in a press release that stockbroking fees were "unfair" and called it the "great retail rip off."
But financial services firm IG – where fees start at £6 – argued that the technology a brokerage provided was crucial and warned on lower-cost providers.
"An investor needs to consider not only the fees a provider charges but also; the price of the stock they (are) buying or selling and the technology their provider has to deliver them a comprehensive and cost efficient service," the company told CNBC via email.
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Hargreaves Lansdown's Cox was cool on the idea that fees could hit zero at some point in the future, arguing that customers are happy to pay for "excellent information and service."
"The rules governing how regulated firms can receive revenues from marketing and advertising are strict. Hargreaves Lansdown has no plans to generate revenue in this way," he added.