Rashford was a strong critic of Mr Williamson’s handling of school meals during the pandemic.
The Cabinet minister said: “We met over Zoom and he seemed incredibly engaged, compassionate and charming but then he had to shoot off. I didn’t want to be the one that was holding him back from his training,”
His team later clarified he had in fact spoken with Camden-born Itoje about laptops for students and equal access to education during Covid.
Retweeting the story, Rashford, 23, said: “Accent could have been a giveaway”, followed by a laughing emoji.
Itoje also joked: “Due to recent speculation I thought it was necessary to confirm that I am not Marcus Rashford… And whilst we are here my name is not Mario either!!
“Just a simple Maro Itoje will do…
“Much love, Marcu… I mean Maro Itoje.”
Mr Williamson said he made a “genuine mistake”.
“Towards the end of a wide-ranging interview in which I talked about both the laptops and school meals campaigns, I conflated the issues and made a genuine mistake,” he said.
“We corrected this with the journalist before publication of the story. I have huge respect for both Marcus Rashford and Maro Itoje who run effective and inspiring campaigns.”
While the sports stars mocked the mistake, others branded it “appalling” and “embarrassing”.
Labour’s shadow education secretary Kate Green tweeted: “Insulting and shocking. Our country and our children deserve better.”
Tottenham MP David Lammy said: “It is depressing that in 2021 one Black man – who has reached the pinnacle of his sport and has given so much back to society – is confused so easily with another by the education secretary.
“Gavin Williamson must be the most ignorant, clueless and incapable Education Secretary in the UK’s history.”
Liberal Democrat MP Daisy Cooper added: “This is a shocking and embarrassing admission.
“If rumours of an imminent reshuffle are true, this must surely be the final nail in the coffin for Gavin Williamson holding ministerial office ever again.”
Rashford’s spokesman confirmed the footballer had never met Mr Williamson.
The Government announced in June 2020 that some 1.3million school children would be given vouchers for free meals during the holidays under the new “Covid summer food fund”.
It followed a passionate campaign by Rashford in which he drew on his own experience of relying on free school meals and food banks growing up.
The Prime Minister’s spokesman said at the time: “This is a specific measure to reflect the unique circumstances.
“Those eligible will be those who already qualify for school meals.”
Earlier on Wednesday, Boris Johnson paid tribute to Mr Williamson for having done a “heroic job” during “very difficult circumstances” when asked whether the education secretary was “up to the job”.
It comes amid speculation Mr Williamson could lose his job as part of a cabinet reshuffle.