Lisanne Beck, 47, and her boyfriend Simon Murphy, 48, were filmed on a mobile phone locked in alleged lewd behaviour at the busy family event on September 14 last year, the court heard.
Music lovers complained after seeing Ms Beck and Mr Murphy together during a set by Paloma Faith.
Beck, a hospitality waitress, and Murphy, a gardener, both of Swansea, deny a charge of outraging public decency.
They have pleaded not guilty to behaving indecently by engaging in sexual activity including oral sex.
Prosecutor Tom Cleeve told the jury the alleged act was seen by nearby members of the public and went "beyond the bounds of public decency".
One onlooker noticed that "other people were getting upset" and there was a young girl who was being "shielded" from it.
The prosecutor claimed the couple were "worse for wear" and seemed to be drunk. It appears that Beck "undid his shorts" and carried out a sex act, Mr Cleeve said.
Security were then called and the couple were ejected from the event.
Beck later denied doing anything wrong, insisting she was just trying to wake up Murphy as they sat on the ground together.
In turn, Murphy has claimed that he was completely unaware of anything indecent happening, the court was told.
The alleged incident happened while Murphy was lying on the ground and Beck had returned to the area, the court heard.
The couple were later arrested and questioned by police. Mike Holden, who took the video clip on his phone, told the court that he was " shocked" by what he saw.
He said: "It was a family event in the middle of the day. It did not seem to be reasonable behaviour. There was a significant amount of embarrassment and trying to divert attention.
"There was one lady who came and actually slapped the lady on her back to try and bring her to her senses ... There was genuine embarrassment as to what we were seeing in Hyde Park."
He said people ranging from eight-year-olds to adults were among the crowd.
Mr Holden said the initial behaviour was "amusing" but it continued and "in my mind a line was crossed that definitely went beyond reasonable behaviour in public".
Mr Holden said that Murphy did not seem to be an active part in what was happening but that he was convinced that something lewd had taken place.
He said: "It was upsetting to a degree, repulsive to a degree and offensive would be appropriate also."
Mr Holden’s girlfriend Julie Conway said she saw Beck “moving her hands around his groin and after that it became quite shocking – she undid his flies”, and appeared to perform a sex act for a minute.
Ms Conway told the court: “The shorts were unbuttoned. From the angle I was at I could see inside his shorts.”
She described the alleged incident as “repulsing, disgusting and unexpected”, adding : “I was shocked and just very concerned. This was a family event, not just for adults.”
One of the onlookers was an off-duty police officer whose wife went to get security.
Norfolk Constabulary Detective Inspector Phillip Gray said the man involved “appeared to be asleep if I am honest”.
He said that “on-and-off” he could “clearly” see Beck put her hand on Murphy’s private parts.
He said: “She leant over and placed her head on his groin area.”
Around this time he noticed a girl who was probably 15 or 16 years old moving away “clearly upset by what was going on”.
There was also an Asian couple nearby and the male “moved the woman away”, Det Insp Gray recalled.
He said he was “disgusted by the fact that it was happening in a concert”.
Security came and helped Beck and Murphy to their feet. It was at this point that he noticed that the front of Murphy’s trousers were wet, he said.
The hearing was adjourned to tomorrow at 10am.