Vote Leave, the official campaign to quit the EU, faces fresh questions over controversial payments it made to other anti-Europe movements during its successful referendum battle.

The Electoral Commission has denied a claim by Vote Leave’s chief strategist, Dominic Cummings, that it had given them “a letter of permission” to make the donations to other campaigns, which are now under investigation.

The commission announced a new investigation last week into donations Vote Leave made of £625,000 to BeLeave and £100,000 to Veterans for Britain, and whether the officially sanctioned organisation had exceeded its official spending limits.

Cummings had previously claimed that the Electoral Commission gave them permission “in writing” to make the donations. However, following months of Freedom of Information requests, the commission has now said it had no record of it. It said it had looked at all correspondence between Cummings/Vote Leave and the commission during the regulated period of the referendum (from April to June) and said: “We can’t find any record of any exchange with us on the subject of donations from that period.”

Cummings failed to respond to the Observer when asked him if he had any explanation for the discrepancy.

The watchdog said that new information meant it had “reasonable grounds to suspect an offence may have been committed” but Stephen Kinnock said it now needed to produce this information. The MP for Aberavon wrote to the commission, the Metropolitan Police and the CPS in the spring with evidence that he claims showed four campaigns were “working together” in breach of UK law. He said: “It’s very unclear what’s prompted this new investigation. They haven’t produced any new evidence beyond what we knew months ago. I think the Electoral Commission really needs to lay its facts on the table. Is Dominic Cummings correct? Was there a letter? Was some sort of deal made? The British public really does deserve to be told.”

The announcement last week came as the commission was facing a legal challenge from the campaigning group the Good Law Project over why it had dropped a previous investigation into the spending of Vote Leave and satellite Brexit campaigns. At stake is whether Vote Leave deliberately engineered a way of exceeding the £7m funding limits mandated by law – and if, as Cummings believes, it had permission to do so. After Jolyon Maugham of the Good Law Project said he would be launch a judicial review of the commission’s failure to investigate the donations, Cummings said on Twitter in September: “FYI u seem unaware (not blaming u no reason u wd know) of a crucial fact: the EC gave us written permission in advance for what we did…” Then: “When they suddenly told us we cd make donations we were so shocked we asked for written confirmation & got it. Extremely surprising…”

The Observer learned of Cummings’s claim in May and had been submitting Freedom of Information requests over a six-month period to try to obtain the letter.

The commission first said it had sent no such letter, then that it couldn’t disclose the information, and finally, when presented with his tweets, that it had reviewed its evidence and its previous response and could confirm it had no record of a letter.

Kinnock said: “There is an unholy alliance of organisations that, at very best, played fast and loose with the law and at worst were deliberately manipulating and cheating. There are so many outstanding questions that I and others have been asking for months.” Kinnock said he had sent another letter to the commission last week raising questions about how all four campaigns – Vote Leave, BeLeave, Veterans for Britain and the Democratic Unionist Party – had appeared to achieve such close convergence in how resources were deployed.

The watchdog said that the new information meant it had “reasonable grounds to suspect an offence may have been committed” and said it would examine if the Boris Johnson- and Michael Gove-fronted campaign had filed its returns correctly.

Electoral Commission guidance requires campaigners to declare if they are working together, to avoid registered campaigns circumventing the spending limits by setting up multiple other campaigns. The guidance states: “Working together means spending money as a result of a coordinated plan or arrangement between two or more campaigners.”