The reports sparked a furious reaction on the Daily Express Facebook page.
One reader commented: “Well Scotland is a part of Great Britain so what’s wrong with that, the Scots do do their own version in the car park at Holyrood with Argos special gazebo and some party balloons, as that’s all they could afford after independence!”
Another fumed: “She is now getting ridiculous, she needs to be reined in, and quick.”
A third blasted: “What is a matter with this woman!”
Another added: “Just more proof she despises the rest of the UK but doesn’t mind taking our cash, no she wants more and more of that.”
A fifth posted: “She’s well suited to the EU, petty, out of her depth, lading her country downwards.”
One more said: “If the Scots want the U.K. and Britain broken up just carry on voting Sturgeon, carry on voting SNP.
READ MORE: Sturgeon SHAMED: SNP caught sitting on emergency welfare fund
The festival has been inspired by the 1851 Great Exhibition and the 1951 Festival of Britain.
At the time, Mrs May said the festival would strengthen “our precious union”.
She said: “Just as millions of Britons celebrated their nation’s great achievements in 1951, we want to showcase what makes our country great today.”
Whitehall sources told Express.co.uk the SNP’s stance on the festival was “quite annoying and frustrating”.
When asked, the Scottish Government refused to say whether requests had been made for the words “UK” and “Britain” to be removed.
A Scottish Government spokesman said: “Ministers haven’t even seen any branding proposals to take a position on and have suggested a similar approach to the pan UK Cultural Olympiad at the time of the London Olympics would work well for this.
“The Scottish Government has engaged constructively from an early stage.”