The Prime Minister has been reported to the Advertising Standards Authority (ASA) over her use of the claims she can draw on a Brexit dividend to boost funding to the NHS.
Shadow culture secretary Tom Watson has written to the advertising watchdog saying the idea there would be significant funds returned to the UK after leaving the EU was "at best misleading and at worst a complete myth".
His intervention follows criticism from the Institute of Fiscal Studies' Paul Johnson, who rubbished the government's suggestion this weekend, saying: "There isn't a Brexit dividend".
However in a major speech yesterday, Theresa May insisted that would be the case.
Speaking from a north London hospital she said: "We are not going to be sending the vast amount of money every year to the EU that we spend at the moment on the EU as a member of the EU.
"That money will be coming back. We will be spending it on our priorities and the NHS is our number one priority."
May went onto reference the phrase Brexit dividend, claiming that while the sums involved were "vast", the £20bn boost she was committing to would also be derived from tax hikes.
The Number 10 Twitter account had also used the phrase in a graphic posted on Sunday.
— UK Prime Minister (@10DowningStreet) June 17, 2018
According to Politics Home, Watson's letter said: "The ASA website states clearly that local authorities, government and other public bodies should be aware that their ad campaigns, like those of commercial companies, are subject to the rules in the Advertising Codes'.
"The thread of graphics posted by the UK Prime Minister Twitter account was an ad campaign promoting the governments policy to millions of followers. The website goes on to say the ASA will intervene if an ad by a public body crosses the line, whether thats through being harmful, offensive or misleading… government departments, local authorities and other public bodies should also ensure that their ads are not misleading and that objective claims are supported by robust evidence'.
"Unfortunately, the Brexit dividend is widely regarded as at best misleading and at worst a complete myth."
He added: "Given the importance of the NHS to the millions of people who follow government advertising on the UK Prime Minister twitter feed, I request that you investigate whether the advertising material breaches ASA policy that advertising has to be supported by the robust evidence."
If the ASA intervenes it would not be the first time a public body has crossed swords with the government over this issue. The UK Statistics Authority has twice rebuked foreign secretary Boris Johnson for his claims that the UK would stop sending Brussels £350m a week, saying it was a "clear misuse of official statistics".