President Trump is due to meet PM Theresa May at 10 Downing Street on July 13.
Campaigners raised almost £18,000 ($24,000) for the helium-filled 20ft high figure, which they said reflects President Trump’s character as an “angry baby with a fragile ego and tiny hands”.
The White House did not comment on the issue.
Former UKIP leader Nigel Farage tweeted that the plan was “the biggest insult to a sitting US President ever”.
Under the plans the inflatable will be allowed to fly for two hours on the morning of Friday, July 13.
Leo Murray, who is behind the crowd-funded idea, said: “[President Trump] really seems to hate it when people make fun of him.
“So when he visits the UK on Friday, we want to make sure he knows that all of Britain is looking down on him and laughing at him.
“That’s why a group of us have chipped in and raised enough money to have a six-metre high blimp made by a professional inflatables company, to be flown in the skies over Parliament Square during Trump’s visit.”
He said organizers initially “didn’t get off to the best start with the mayor’s office over this, who originally told us that they didn’t recognize Trump Baby as legitimate protest”.
However, Leo Murray said City Hall had “rediscovered its sense of humor – Trump Baby will fly”.
A statement on behalf of the London mayor said Sadiq Khan “supports the right to peaceful protest and understands that this can take many different forms”.
Sadiq Khan’s city operations team met organizers and gave them permission to “use Parliament Square Garden as a grounding point for the blimp”.
More than 10,000 people signed a petition calling for the inflatable to be given permission to fly, activists said.
Sadiq Khan and Donald Trump have repeatedly clashed on Twitter, including in the aftermath of the London Bridge attack.
Before the inflatable can take off, campaigners will also need permission from the National Air Traffic Service (NATS) as the project constitutes a “non-standard flight in controlled airspace”, a spokesperson said.
Because Parliament Square sits within restricted airspace, additional approvals are also needed from the Metropolitan Police.
Max Wakefield, who is one of the people working on the project, said the group is “confident it will obtain all necessary permits”.
He said the initial crowd-funding target was just £1,000 ($1,300), but this was reached within 24 hours.
The extra cash will now be used to send the balloon on a “world tour” and “haunt” President Trump wherever he goes, Max Wakefield added.
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