The Department for Business, Innovation and Skills (BIS) is taking the step out of concern that the voluntary approach taken so far in its "midata" initiative is proving too slow.
British Gas, Google, Lloyds, Moneysupermarket.com, Three and Visa are among 13 consumer brands which have backed midata since it was launched in April 2011.
However, the fact that no retailers have signed up is a concern for BIS, which is understood to have held talks with Tesco.
BIS is now investigating the possibility of enacting legislation giving it the power to compel participation.
In response, the Direct Marketing Association welcomed BIS attempts to push forward the programme, but urged companies to take the initiative on opening up data themselves as a form of "competition-based self-regulation".
The consultation, which closes on 10 September, asks businesses for information to help it "get the details right, so we can have an effective implementation of midata that will remain relevant in the future".
Further consultation would be necessary before the power could be exercised through secondary legislation, according to BIS.
Norman Lamb, the consumer minister, said: "It's clear to me that giving consumers the right to access their own transaction data promises huge opportunities for both consumers themselves and UK businesses.
"We want the UK to be at the forefront of the data analytics and information services market that is rapidly growing, with huge international potential. However, it’s crucial that we engage with business and consumers to ensure that we do this in the right way."
The 26 supporters of midata also include intermediary organisations such as Billmonitor, regulators such as the Information Commissioner’s Office, Ofcom and the Office of Fair Trading, and consumer groups including Citizens Advice.
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