Marek Zakrocki, 48, staged the attack outside Spicy Night in Alexandra Parade in Harrow, north-west London, on 23 June.
He was heard saying: “I’m going to kill a Muslim. I’m doing it for Britain. This is how I’m going to help the country. You people cannot do anything.”
The Old Bailey heard that the Polish-born window fitter then used his white van as a weapon against Kamal Ahmed and mounted the pavement twice.
He was driving at 5mph and was effectively trying to pin Mr Ahmed against the front of the restaurant window, which smashed.
Following his arrest by armed officers, police found a Nazi coin in Zakrocki’s pocket and a stash of Britain First flyers and newspapers at his home in Harrow.
Theresa May told Trump he was “wrong” to share the post, to which the President responded angrily that Mrs May should concentrate on fighting extremists rather than concentrating on his actions.
At the Old Bailey on Monday, Zakrocki pleaded guilty to dangerous driving and beating his wife.
Prosecutor Denis Barry said: “Mr Zakrocki had plainly, during the course of that afternoon, had far too much to drink.
Mr Barry said Zakrocki had been “fixated” by Muslims and had made donations to Britain First in the past.
Because of the increased state of alert at the time of the incident, armed police arrested Zakrocki in a “hard stop”.
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Mr Barry said the defendant appeared to have a history of depressive illness and alcohol problems.
Earlier on June 23, he had grabbed his wife Ewa Zakrocka’s arm and threatened to “kill people” and then kill himself.
Mr Barry said: “Because of the time that all this took place, the police took what had happened particularly seriously and there was a hard stop by armed police officers.”
He told the court that Britain First, formed by members of the BNP, was anti-Muslim and held views that were regarded by most people as “very extreme indeed”.
Further charges of attempting to cause grievous bodily harm and having a knife in Northolt Road, Harrow, were ordered to lie on file.
Judge Anthony Leonard QC will sentence the defendant at the Old Bailey later on Monday.