Digitonomy Ltd sent over five million unsolicited messages encouraging people to apply for cash loans via affiliates.
Investigating 1,464 complaints about the texts made between April 2015 and February 2016, the Information Commissioner's Office (ICO) found the company could not prove it had consent.
A company spokesman apologised to those people who found the texts "unwelcome".
The ICO's investigation revealed the company had used affiliates to send the messages and claimed they had proof of consent.
The ICO's head of enforcement Steve Eckersley said the wording of the consent examples were not sufficient and businesses that rely on direct marketing "must be able to confirm that people have given their permission to receive text messages".
"Depending on the word of another company is simply not acceptable and is not an excuse," he said.
A spokesman for Digitonomy said the company was "sorry that a reported 0.03% of recipients found the marketing messages from our appointed affiliate management company last year unwelcome".
He added that the company remained "determined to operate at all times within both the spirit and the letter of the law and best practice".

The singer had forgotten about the work, entitled Little Electric Chair, presented as a gift in the 1970s.
"It was a rock 'n' roll time, none of us thought about anything," Cooper's long-time manager, Shep Gordon, said.
A similar version of the Warhol artwork sold at Christie's in New York in 2014 for $10.5m (Â£8m).
Cooper's find, a red silkscreen on canvas, was part of Warhol's Death and Disaster series and was discovered "rolled up in a tube" in a locker along with a collection of 1970s stage props, Mr Gordon told BBC Radio 5 live.
It was the decade that Cooper and Warhol met and became friends. "It was all a swirl of drugs and drinking," said Mr Gordon, who has been the singer's manager for more than four decades.
Cooper, real name Vincent Furnier, moved to New York with his late girlfriend Cindy Lang, where they were introduced to Warhol and spent time together in New York's famed Studio 54 nightclub, according to Mr Gordon.
Ms Lang, who appeared on the second cover of Warhol's magazine Interview, later asked Mr Gordon to purchase the work on her behalf for about $2,500 as she planned to present it to Cooper as a birthday gift.
"He was a very heavy drinker in those days," Mr Gordon told the BBC, adding that Cooper's career was "like a rocket ship taking off back in the early 70s - he was working 100 shows a year".
Mr Gordon said the rock singer was "getting electrocuted" at the time in his live shows using a prop electric chair that looked "very much" like the chair in the painting.
He said that Cooper later entered rehab as a result of his drinking and "never really moved into his apartment in New York". The painting, he said, was forgotten.
"Nobody really ever thought about it, life went on," Mr Gordon said.
Years later, Mr Gordon was having dinner with friends, one of whom happened to be an art dealer, when the conversation turned to a piece of work by Warhol that had sold for a large sum.
"So I got hold of Alice and I said: 'Do you still have that Warhol?' And he said: 'I don't think so'."
Mr Gordon said it was months before they tracked it down to the storage facility. "And then we found a tube, like the type you keep posters in, and there it was - oops!"
He said that back in the early 1970s the artwork was not considered particularly valuable. "Andy Warhol was not 'Andy Warhol' back then," he said.
The artist died in 1987 at the age of 58.
In an interview with the Guardian, Mr Gordon said that Cooper had a vague recollection of discussing the artwork with Warhol.
"He thinks the conversation was real, but he couldn't put his hand on a Bible and say that it was," Mr Gordon said.
The work has been confirmed as authentic by Warhol expert Richard Polsky.
"You should have seen Alice's face when Richard Polsky's estimate came in," Mr Gordon said, adding: "His jaw dropped and he looked at me: 'Are you serious? I own that!'"
A Chester credit broker has been fined £120,000 for sending millions of text messages without permission.
[NEXT_CONCEPT]
US rock musician Alice Cooper has found a classic Andy Warhol artwork rolled up in storage after more than 40 years tucked away alongside tour equipment.