Ciro's Place and Fryin' Brian were originally told to vacate the Market Square by 8pm on April 24 after WNC terminated their trading arrangements.
In a letter sent to the traders in April, the council said "changes are required to the standards, mix and overall quality of trading operating on the square as part of an ongoing place shaping and market improvement programme."
The letter also stressed the decision was "not a disciplinary action" and was "not based on any single complaint or allegation against you personally."
The council initially linked the decision to allegations of anti-social behaviour before later withdrawing that explanation and instead citing the wider market improvement programme.
On May 11, the council gave both traders a final deadline of May 15, warning they would face legal action if they failed to leave. However, no action followed and both businesses have continued trading.
As of Monday July 6, the food vans remain in place.
Asked for an update, a WNC spokesperson told the Chronicle & Echo: "The Council has issued court proceedings in accordance with the existing tenancy at will, and the claim is currently progressing through the court's administrative process."
Responding to the update, Ciro's Place owner Joao said he was not surprised.
"I never believed the council would back down from this," he said.
He said he still had not been given a clear explanation for why his business had been selected.
"I've said I'm happy to leave if I have to. I just want to know why I have to go.
"I've been working with the council for years. I pay my rent and I still don't understand what's happened.
"I can't understand why they've decided to get rid of the two busiest businesses in the market and leave the ones that aren't as busy. Is it a bad thing to be busy?"
Speaking about the legal action, he said: "I knew it was coming. I don't know what I'm going to do now. Move, stay or fight it – I honestly don't know.
"I feel defeated. You always hope something might change, but logically I knew they were never going to back down."
Fryin' Brian owner Paul said he has also not been given a reason for being asked to leave.
Customers also criticised the council's handling of the situation.
One customer said: "It's disgusting. They need to grow a backbone and come and talk to Paul and Joao about what's going on."
Another added: "It's not very professional. They've not given any valid reason for them to leave."
