Parry, 45, of no fixed abode, was convicted of one count of stalking.
He had also denied impersonating a police officer by flashing what Sir Gavin said appeared to be a warrant card and making comments about arresting him on the June date.
District judge Tan Ikram found there was no case to answer with respect to the police impersonation charge because the evidence was “so poor”.
The judge said: “I am satisfied that those two occasions taken collectively amount to harassment of Sir Gavin.
“The defendant thinks there is humour in relation to what he does. He uploads it onto social media.
“Objectively he ought to have known the course of conduct amounted to harassment. I am sure of that.”
Giving evidence at City of London Magistrates’ Court on Wednesday, Sir Gavin told of how Parry began following him along streets in Whitehall on two occasions after the MP walked past a protest area opposite Downing Street.
Of the May incident, Sir Gavin told the court he heard Parry making comments about vaccinations while walking in “close proximity” to him.
Asked how he felt at the time, Sir Gavin said: “It was someone who was quite aggressive towards you, someone who was not really actually wanting to have a discussion, but rather express their views or their anger or their dissatisfaction, actually.
“It felt very unpleasant.”
He added: “Of course as an MP you get a lot of people approaching you all the time.
“People are often approaching you with concerns they want to discuss… (but) done in a very different manner to that.
“You felt as if this was part of intimidation or sort of trying to make a publicity work or something along those lines.”
Of the June incident, Sir Gavin said he heard Parry making comments about vaccinations again and also about “genocide”, and eventually realised that the comments were directed at him.
The MP kept walking and speaking with a constituent on the phone, he told the court.
He called Parry’s “persistence” in following him from the Parliamentary estate towards Euston “quite disturbing”.
“It was quite evident that this individual was hostile to myself,” Sir Gavin said. “I was talking to a constituent who sadly that day had had to have their dog put down.”
He continued: “Why should I, you know, not do what I thought was my job because this very aggressive person was harassing me and pursuing me?”
The politician then went on to explain how he believed Parry flashed a warrant card and spoke about arresting him.
“At this point, it is getting to feel kind of more scary because it’s a confined space,” he said.
“I can hear constant references to police, police, police, and saying about arresting me and at this stage … the defendant then shows what looks like a police a Metropolitan Police badge, but it was just a crest.”
“I felt incredibly threatened by it,” he added about the June incident.
Parry denied intending to harass, distress, humiliate or intimidate the politician over the two dates when he gave evidence on Wednesday.
He appeared at court with Piers Corbyn, the brother of former Labour leader Jeremy Corbyn.
Parry will be sentenced at Westminster Magistrates’ Court on November 16.
Sir Gavin has been MP for South Staffordshire since 2010 and served in cabinet as defence secretary before becoming education secretary under Boris Johnson in 2019.