A new amendment to the data bill that would require artificial intelligence companies to disclose their use of copyright-protected content has been tabled, after MPs voted to remove an earlier version on Wednesday.

The amendment by the cross-bench peer and former film director Beeban Kidron will be a fresh challenge to plans to let artificial intelligence firms use copyright-protected work without permission.

It circumvents the financial privilege grounds – meaning there is no budget available for the regulation – on which its predecessor was rejected..

The new wording states the government “may” make enforcement provisions rather than “must”, and gives no detail about how the government could enforce them.

It will be put to peers in the House of Lords for debate on 19 May after the earlier version of the amendment passed by 272 votes to 125 in a debate on Monday.

Lady Kidron said: “We have accepted the speaker’s ruling on the Commons financial privilege and replaced the original amendment with another that would still offer transparency.

“We very much hope that the government will accept it because it is in line with the review that they have proposed and the transparency that they have repeatedly said is a key to the outcome. But what it offers the creative industries and UK AI companies is a clear timeline, and a mechanism by which licensing and not stealing can become the norm.”

Owen Meredith, chief executive of the News Media Association, said: “This new amendment removes any potential direct spending implications for enforcement – which was the Commons’ objection to the previous drafting – and would ensure copyright owners receive clear, relevant, accurate and accessible information about how their work is accessed and used, but gives the government flexibility over exactly how this is achieved.

“The entire creative industries, the voting public, and multiple parliamentary reports and debates have given a clear view to the government that action now to ensure rights holders are better equipped to enforce the existing law, with the proportionate application of transparency, is a progressive way forward. It’s time to act, not just ‘listen’.”

In Wednesday’s debate, the data protection minister, Chris Bryant, told MPs that although he recognised that for many in the creative industries this “feels like an apocalyptic moment”, he did not think the transparency amendment delivered the required solutions, and he argued that changes needed to be completed “in the round and not just piecemeal”. He added that the sooner the data bill was passed, the quicker he would be able to make progress on updating copyright law.

The government’s copyright proposals are the subject of a consultation due to report back this year, but opponents of the plans have used the data bill as a vehicle for registering their disapproval.

The main government proposal is to let AI firms use copyright-protected work to build their models without permission unless the copyright holders opt out – a solution that critics say is unworkable.