British Foreign Secretary Boris Johnson made a rallying cry for Brexit on Friday in what will be viewed as a challenge to Prime Minister Theresa May, one week before her own big speech on the subject.
The £350m figure was a major feature of the Leave campaign during the European Union referendum in 2016.
Boris Johnson has renewed the claim that the United Kingdom will have £350m per week to spend on the NHS after Brexit.
In the run up to the referendum, it said the number lacked "clarity" because it referred only to the UK's gross annual contribution and did not take into account Britain's rebate, or money that comes back from the EU.
Mr. Johnson, a former journalist, wrote a 4,000-word article in the Saturday edition of The Daily Telegraph newspaper to explain how Brexit can bring a "glorious" future to Britain and help it become "the greatest country on Earth".
Mr Johnson has written to Sir David saying he is "surprised and disappointed" about the statistics chief's letter criticising his article.
"There are two stages before you get to that - first of all we need to agree the quantum of money that will be available to spend after we leave and secondly we need to decide how to spend that", said Green.
"Once we have settled our accounts, we will take back control of roughly 350 million pounds (475 million USA dollars) per week".
The Labour MP Chuka Umunna, a leading supporter of Open Britain, said: "Yet again Boris's outright lying has been exposed by Britain's statistics watchdog".
Lib Dem leader Sir Vince Cable said: "I'm glad to see the independent UK Statistics Authority has the courage to slap Boris down. He has not changed the conclusion set out in his letter to the Foreign Secretary".
Damian Green, a close ally of the prime minister, told Radio 5live's Pienaar's Politics, that the timing of Mr Johnson's article "could have been better for all sorts of reasons not least the awful terrorist incident we've had".
Amber Rudd has accused Boris Johnson of backseat driving as she questioned the timing of his 4,000 word vision of Britain's departure from the European Union and made clear that she did not want the foreign secretary managing the Brexit process.
But it was widely derided in the weeks after the result, and Mr Johnson and other campaigners appeared to distance themselves from the promise.
The prime minister is due to make a major speech on Brexit in Florence, amid speculation she is prepared to announce some kind of deal on transitional trade payments.