Suspecting there was more to it the pair, who are of British-Bangladeshi and British-Pakistani descent, decided to investigate further.
After leaving, Rajina and her friend decided to phone the restaurant using a "white accent" to try and book a table.
"I phoned the restaurant to see if I could get a table if I put on a white-sounding voice.
"Straight away, the woman on the phone said they had tables free and we should come within five minutes."
Furious with their treatment, Rahman then challenged the woman as to why he was refused a table just minutes earlier and asked if it was to do with his race.
"She got really flustered and said if we came straight away she would give us one but obviously we said 'well we don't want the table now' and told her that we would be taking it further," Rajina said.
The woman then allegedly hung up.
Rajina took to Twitter to vent about the incident.
Rajina feels the attitude from the restaurant's staff members reminded her of the vile abuse minorities put up with in past generations.
"It reminded me of things when my parents were young, when there used to be signs on restaurants saying 'no Irish, no blacks, no dogs'."
Following the incident, the pair have written reviews on TripAdvisor, Google and Facebook, and Fatima says she wants an apology from the company.
A spokesman for Cote said: "We are taking this allegation very seriously."