The group of 16 were turned away by French authorities at Folkestone after attempting to travel to Calais on the Eurostar shuttle service on Saturday afternoon.
It happened on the same day as an aid convoy made up of around 250 vehicles was held at the port of Dover after being refused entry to France by authorities.
The convoy, organised by a number of campaign groups including the People’s Assembly and Stop the War Coalition, left London on Saturday morning before being prevented from boarding ferries to Calais by French authorities.
The lorries, cars and minibuses were carrying aid donations for refugees and migrants living in the Jungle camp in Calais.
Freelance journalist Liz Smith, 34, of Chapel Allerton, Leeds, was travelling in a mini-convoy with the 16 volunteers from Leeds.
Ms Smith, who was allowed into France because she is a member of the press, said: “The French police took the passports from our group and tried to make them sign forms saying they were a threat to national security.
“They also put refusal of entry stamps on people’s passports. They were quite scared. They didn’t want to sign the forms because there was no translation in English.
“They were turned back and escorted away from the port by police. I think it is absolutely ridiculous. We weren’t part of the main convoy and we were obviously delivering aid.
“They let football hooligans through, but not people delivering aid.”
Student Alex Claxton-Mayer, 21, of Chapeltown, was among the group turned away by French authorities. She said: “I feel it’s disgraceful to stop ordinary people taking supplies to destitute people.
“I was disgusted that the French border police wouldn’t allow us to take tins of soup and beans to the refugees.
“To add insult to injury, we don’t know if we will be allowed back in to take the supplies on another day.”
In a statement the prefecture of Pas-de-Calais cited a number of reasons for issuing the ban, including the potential for it to “generate violent episodes” and the lack of police officers available because of the ongoing European Championships.
They also said the numbers of vehicles involved may “facilitate the intrusion of migrants”. It added: “In these circumstances, the Prefect of Pas-de-Calais considered only the prohibition of any event is likely to effectively prevent public disorders that may occur. Moreover, any convoy on roads and highways, from Great Britain to Calais to slow or block the flow and constituting a public event, is prohibited.”
Mussa Mahdy, 65, a refugee at the Jungle camp in Calais, said: “We said we wanted them to come because they were coming to help We don’t know why the French government wouldn’t let them come here because we said we wanted them to”