The chairman of the Financial Conduct Authority has questioned the extent to which consumers are able to make informed decisions.
He said the increasing use of online services meant consumers were having to wade through growing numbers of terms and conditions.
This meant the traditional liberal approach to markets - which rests on the assumption a consumer can and will make good choices if they are given fair disclosure - could be called into question.
Mr Randell said this meant the growing use of Big Data and artificial intelligence ran the risk of disenfranchising consumers, rather than empowering them.
He said: "Research conducted in the US some 10 years ago estimated that if the typical individual using online services actually read the privacy policies before clicking ‘Agree’, she would spend around 250 hours per year doing so. That is about six working weeks every year.
"Imagine how many weeks you would have to spend to read all the terms and conditions you click through today, given the growth of online services in the last 10 years.
"The power of Big Data corporations and their central place in providing services that are now essential in our everyday lives raise significant questions about the adequacy of global frameworks for competition and regulation.
"The ordinary consumer may in practice have no choice in whether to deal with these corporations on terms which are non-negotiable and are often too general to be well understood. And without access to the data which consumers have signed – or clicked – away, new businesses may find it very difficult to compete."
To illustrate this issue, Mr Randell highlighted recent FCA concerns that firms in the general insurance market were using their predictions of customers' propensity to shop around to impose significant price rises on those who do not.
He also cited media reports earlier this year that price comparison websites quoted significantly higher car insurance premiums for people with names suggesting they are members of ethnic minorities.
Mr Randell said: "Some may say 'caveat emptor', or ask why firms should not maximise their profits using all means at their disposal. But I don’t think that would be the prevailing view in our society."
He said firms using consumers' data needed to engender more trust, but doing so would require good communication to make sure consumers understood and accepted a firm's approach.
Mr Randell added: "By good communication, I don’t mean pages and pages of obscure disclosures, disclaimers and consents. I mean short and readable statements which make it clear what firms will and won’t do with their customers’ data."
Mr Randell, a former lawyer, became chairman of the FCA in May, taking over from John Griffith Jones.
Clayton Cumming, a partner at Advice & Wealth Management Solutions, said: "It is ideal to condense recommendation reports and terms and conditions down but you are also highly regulated. It is a Catch 22 situation.