Jordan Horner and another Islamic extremist told one couple they could not hold hands while walking down the street, because it was in a 'Muslim area'.
The radicals also attacked a group of men drinking in the road, and told a woman she would face 'hell fire' because of the way she was dressed.
Horner, 19, Ricardo MacFarlane, 36, and a 23-year-old man who cannot be named for legal reasons were sentenced to 68 weeks, 12 months and 24 weeks in prison respectively.
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Jailed: Jordan Horner, and Ricardo MacFarlane, have been sentenced to prison along with another man for their role in the self-styled 'Muslim Patrol'
The court earlier heard that last December Horner and the 23-year-old man drove alongside Joshua Bilton and Anna Reddiford in Bethnal Green, and started yelling at them through a megaphone.
The teenage convert shouted: 'Let go of each other's hands. This is a Muslim area!' - but the couple initially assumed it was a joke.
They stopped holding hands after the men repeated the message - and when they started again, the car blocked their way until they let go.
Two weeks later, Horner and MacFarlane attacked men drinking in Shoreditch, shouting: 'Kill the non-believers.'
Horner then punched two of the group, hitting James Forward in the jaw and knocking out Patrick Kavanagh with a sucker punch to the head.
On January 13, Horner and the 23-year-old harassed another couple, Clare Coyle and Robert Gray, as they were walking in Stepney - accusing Miss Coyle of being a 'slag'.
In an exchange filmed on Horner's phone, she replied, 'This is Great Britain. I can dress how I wish,' while the group shouted: 'Remove yourselves now. Muslim Patrol. Move away from the mosque.'
Horner, an associate of hate preacher Anjem Choudary who has declared he wants to bring Sharia law to Britain, pleaded guilty to two charges of assault and two charges of using threatening words and behaviour.
He was jailed earlier this year for beating up a photographer, and has been seen putting up posters across East London 'banning' alcohol.
MacFarlane, who pleaded guilty to affray, has previous convictions for criminal damage for painting over advertisements of women in the street.
The 23 year-old admitted two counts of using threatening words and behaviour.
Prosecutor Alex Chalk told the court: 'This is a case about religious vigilantism. These men were members of a self-styled Muslim Patrol who threatened, intimidated and even assaulted members of the public who they perceived to be behaving in an un-Islamic manner.
'The men accosted members of the public in neighbourhoods of East London which they claimed were Muslim areas, and where according to them different law applied.'
Radical: Horner, 19, is close to jihadist hate preacher Anjem Choudary, pictured during a demonstration
Judge Rebecca Poulet QC told them: 'One of the many good things about living in Great Britain is the tolerance and respect members of the public generally show to one another's religious beliefs, his dress or his chosen way of life.
'When on occasions a person shows their intolerance of another individual whether by aggression or violence and in such a way as to cause real fear to the individual then the law can be invoked to protect that individual.
'This law would protect you if someone treated you in this way. It is the very same law that now brings you before this court for your conduct.
'My understanding is that Islam is a peaceful religion and this conduct was unfortunately anything but.'
Lisa Wilson, representing Horner - who calls himself Jamal Uddin - said: 'He recognises that the offences are serious and recognises the custodial threshold is clearly passed.
'Actual bodily harm were of course serious and people were harmed. The incidents themselves lasted for a very short duration.
'Mr Uddin for his part felt provoked. He has three previous convictions all committed in 2010, he was a drug user and his life has changed since then - he has found a religious calling.
'He has a wife and two children, a 14-month-old son and a daughter born six days ago.
Up until now he has been a young man who was immature and easily led.
He now wants to work in the retail sector.'
Susan Meek, representing the 23 year-old, said: 'He is a relatively young man, he has an offending history a lot of it is prior to him converting to Islam - this offending relates to his religious choice.
'He said he didn't think about the effect it would have on the victims, didn't think about the consequences and he has said he feels very stupid.'