The woman tries to respond and a flight attendant can be seen trying to calm the situation.
A man took it upon himself to intervene during the incident trying to calm the angry passenger.
It has referred the matter to Essex Police.
The woman's 53-year-old daughter told the Huffington Post that they were returning from a holiday created to cheer her mother up, a year after the death of her father.
"It is great that David did film that", she said.
Then the man shouted at the woman while her daughter told him her mother was disabled.
The woman can be heard telling the man that he stinks and he needs a wash, before asking to be moved so she can sit next to her daughter.
It's really important to point out that cabin crew have very little authority to reprimand or even restrain a disruptive passenger when an aircraft is on the ground - that's the job of the police or security services.
The bully starts prodding the empty space between them, shouting at crew to "put her in another seat".
A VIDEO appearing to show an elderly woman being subjected to racist abuse on a Ryanair flight has drawn widespread condemnation.
He replies: 'I don't care whether she's f****** disabled or not - if I tell her to get out she gets out'.
Mrs Gayle's daughter told the Huffington Post her mother had "been feeling really down and depressed, so I thought the trip would raise her spirits".
"In fact, one of the passengers whilst I was filming basically said to me don't you think you're being a bit childish by filming this", he said.
Another man can be heard saying "throw him off the flight".
Mr Lawrence told the BBC he was shocked the airline allowed "something like this to go unchecked".
Other politicians are also calling for action from Ryanair, including shadow minister Karl Turner.
Critics of the incident and how it was handled said the man should have been removed - rather than the woman herself moving seats.
The budget airline tweeted on Sunday that it is aware of the incident and has reported the matter to the Essex police. "He suggested that we make a formal complaint to Ryanair".
Anyone with information can contact Crimestoppers anonymously on 0800 555 111.