Authorities have told the Banbury Guardian the facility had not opened today because of icy conditions.
Jacqui Broadbent and many other parents drove to the PCR testing centre at Bodicote House, having been offered that option on an online appointments system today (Monday).
But when the parents, and others, got to the district council offices car park, there was no testing operation there and they all turned around and left.
Parents of children in Year 9 at Blessed George Napier School had been sent letters to say there had been an outbreak of the virus in that year group and many wanted to have their children tested.
Mrs Broadbent told the Banbury Guardian: "Families of pupils at BGN school, and others, have gone to Bodicote House and there was no one there, so we've got to find somewhere else to get the test. We drove in and there was no white tent, no sign posts, no marquee, nothing. We all had to turn around and drive away again.
"I rang NHS Test and Trace and they said they can't do anything about it. I'm told the Bodicote one was in action last week. What are we meant to do? We hear that there is a huge rise in cases in and around the town."
The Banbury Guardian attempted to make an appointment and the Gov.uk website gives the Oxford Parkway Park and Ride as a drive through testing centre and continues to offered the Bridge Street testing centre, which closed in October 'temporarily'. The Oxfordshire County Council Covid web page lists Bodicote House as a testing centre every day from 9am - 3pm.
A spokesman for Cherwell District Council said: "On Monday, November 29 Cherwell District Council was advised that the mobile testing unit would not be available because of icy conditions. We are expecting it back at Bodicote House on 30 November.
"People can book a test or have one delivered to them at home by visiting www.gov.uk/get-coronavirus-test."