Information provided by Boris Johnson to an inquiry into his relations with a US businesswoman as London mayor has been deemed “insufficient” to resolve issues raised.

The prime minister’s response to a demand for details of his contacts with Jennifer Arcuri was handed over by his lawyers to the London Assembly oversight committee late on Tuesday.

But the committee said it was “frustrated” by the secrecy displayed in the PM’s submission and is now considering issuing a summons for Mr Johnson to give evidence in person - and could publish his letter.

Chair Len Duvall said the committee was “at this stage” respecting a request not to publish Mr Johnson’s response, but was seeking further information from the PM.

The committee, which oversees ethics at the Greater London Authority, opened an inquiry following allegations in the Sunday Times that Ms Arcuri was given public money and preferential access to business missions overseas after striking up a friendship with Mr Johnson.

In a letter last month, they demanded details of all professional, social and personal contacts by the then mayor with the tech entrepreneur, as well as an explanation of how the alleged relationship was disclosed in dealings with the GLA.

The PM has said that he made no declaration of interest at the time because there was “no interest to declare”. Neither he nor Ms Arcuri have responded to claims that she told friends at the time that they were in an intimate relationship.

Oversight committee chair Len Duvall said: “The role of the London Assembly is to ensure that City Hall is above question and we must abide by the ethos of complete openness and transparency.

“We did finally receive a response from Boris Johnson, through his solicitors, which they have indicated may not be published. At this stage we are respecting that, but we are seeking further clarification.

“Nothing in the response, in our opinion, reflects the need for confidentiality. In fact, the response is insufficient as far as our request for information is concerned.

“We are focussed on our investigation and considering next steps. A number of options are open to us; they include speaking to various people and using our power of summons.”

Mr Duvall said the committee was liaising with the Independent Office for Police Conduct, which has been asked by the GLA to look into whether Mr Johnson could face a charge of misconduct in public office.