UK taxpayers have paid out more than £34,000 to cover the cost of the science secretary Michelle Donelan’s libel case, the Guardian can reveal, more than double the sum the government had previously admitted.

The legal fees racked up by the cabinet minister after wrongly accusing an academic of supporting or sympathising with Hamas cost the public an additional £19,000, on top of the £15,000 libel settlement.

The revelation last month that the Department for Science, Innovation and Technology (DSIT) would cover the cost of Donelan’s libel prompted political anger over the use of public money.

She faced calls to resign from opposition parties and criticism from Tory backbenchers as she was urged to cover the cost of settling the libel action herself after apologising and publicly retracting her remarks.

The department declined at the time to disclose Donelan’s legal costs. However, a letter from the top official at the department, Sarah Munby, to the shadow science secretary, Peter Kyle, has now revealed the overall bill.

The letter showed that in addition to the costs incurred by the government’s legal department of £7,785 for internal legal advice, Donelan sought external private legal counsel which cost a further £11,600.

Munby, the DSIT permanent secretary, confirmed that civil servants, including lawyers, provided advice and clearances to the cabinet minister, but did not divulge the contents of this advice.

In response to the letter, Kyle said: “It’s a slap in the face to hardworking families up and down the country that over £34,000 of taxpayers’ money was wasted on unprofessional and libellous behaviour from a Conservative cabinet minister.

“Instead of trying to cover up the true cost of her actions, Michelle Donelan should have had the decency to pay the money back to the taxpayer.”

Donelan apologised and paid damages last month after accusing two academics of “sharing extremist views”, and one of them, Prof Kate Sang, of Heriot-Watt University in Edinburgh, of supporting Hamas.

Sang launched a libel action against Donelan after the minister published a letter to UK Research and Innovation (UKRI) on her private account on X, urging it to cut links with Sang and Dr Kamna Patel, of University College London.

Donelan had described her “disgust and outrage” at their appointment to an expert advisory group to Research England on equality, diversity and inclusion.

UKRI suspended the advisory group’s operations while it carried out an investigation into the allegations. It found no evidence to back her complaints against the academics, or any grounds to remove them from the advisory group.

UKRI, which is an arm’s-length body funded by the taxpayer, disclosed last month in a freedom of information response that it spent £15,000 including VAT on the investigation and more than £8,200 on legal advice.

It means that overall, UKRI and the UK government have spent more than £61,460 as a result of Donelan’s remarks.

Donelan’s evidence included Sang retweeting a Guardian article from last October headlined: “Suella Braverman urges police to crack down on Hamas support in UK”, to which Sang added the comment: “This is disturbing.”

In her statement last month, the senior Tory said she had been mistaken in taking this to mean support for Hamas, and that Sang’s comment had been about the article more widely.

The DSIT admitted last month that it had paid the damages and legal costs, adding: “This was subject to all the usual cross-government processes and aims to reduce the overall costs to the taxpayer that could result from protracted legal action.”

The DSIT has been approached for comment.