But Mr Johnson hit back in a strongly-worded letter of his own, accusing Mr Norgrove of a "wilful distortion of the text of my article".
"What I would say is if you do shoot yourself in the foot on this issue, then that bullet was very much worth it, and your foot will no doubt recover in due course but gosh it need to be done - because we can not afford to muddle this Brexit thing up". I suggest if the BBC coverage offends you that you write to the BBC.
Rudd said: "What I meant by that is I don't want him managing the Brexit process".
In his Daily Telegraph article on Saturday, Mr Johnson wrote: "Once we have settled our accounts, we will take back control of roughly £350 million a week". "It would be a fine thing, as many of us have pointed out, if a lot of that money went on the NHS (health service)".
"That is very different from claiming that there would be an extra £350m available for public spending and I am amazed that you should impute such a statement to me".
UK Foreign Secretary Boris Johnson has been criticized by Chair of the UK Statistics Authority David Norgrove for his newspaper article, in which he claimed that Brexit will allow London to save hundreds of millions of pounds each week.
On a fast-moving day, the Prime Minister was forced to interrupt her trip to Canada to slap down her Foreign Secretary, reminding him that her government was "driven from the front".
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Mr Johnson's decision to release the article six days before Mrs May is due to set out her plans for Brexit in a speech in Florence prompted claims by allies of the Prime Minister that the move was "hostile" and "attention- seeking".
Johnson, who is set to meet May in a showdown meeting in NY ahead of her address to the UN General Assembly, repeated his stance on Monday that he would not support any payments to the European Union after Brexit in March 2019.
Sir Craig Oliver, former director of communications at Downing Street for David Cameron, said even if the genuine intention was to support the Prime Minister, it was obvious it would be seen in Westminster as a "direct challenge".
Johnson's only comment since his Telegraph article was published was on Twitter, where he said he was "looking forward" to May's speech in Florence later this week.
Johnson, however, did suggest to curtail foreigners buying homes in London, borrowing more to upgrade the UK's infrastructure, and a tax reform.
Last month, EU Chief Negotiator Michel Barnier also warned that Britain would be forced to leave Europol and that the EU-UK split would weaken British security and counter-terrorism.