Mr. Bullock, one of Mr. Downey’s new customers, said that Bloomberg had long been the subject of complaints among his colleagues, who criticize the company’s unwillingness to negotiate on the price of terminals, even when companies are paying for hundreds of them.

Bloomberg has been able to remain firm on its prices because the terminals have had few significant competitors other than Thomson Reuters.

Thomson Reuters has made several efforts to revamp its terminal to take on Bloomberg’s dominance among elite traders and has had success in certain niches, like foreign currency trading. But Thomson Reuters terminals are not notably cheaper than Bloomberg’s, and the company has continued to lag in the United States — where its revenue was only two-thirds that of Bloomberg, data from Burton-Taylor shows.

Other competitors, like Markit and FactSet, are cheaper but have tried to challenge Bloomberg only for smaller corners of the markets.

Mr. Downey said that banks had been frustrated with Bloomberg prices for a long time, but had become more active in looking for alternatives since Bloomberg was accused in 2013 of allowing its journalists to snoop on some personal details of customers.

A 42-year-old Irishman, Mr. Downey is largely paying Money.Net’s costs with the proceeds from his lucrative first career as a commodities trader. He is reluctant to reveal his client numbers, but so far he counts them in the thousands, not yet enough to scare Bloomberg. Mr. Downey, though, has big ambitions, and at least some of his new customers have been impressed enough that they have essentially served as volunteer boosters for the company.

Hamza Khan, the 28-year-old head of commodities strategy at ING Bank in Amsterdam, said that since his company signed up last year, Money.Net has not been able to do everything that a Bloomberg can. But it has all the essentials and offers a more modern and intuitive interface and user experience than the Bloomberg system, he said.