Emergency timetables would mean fewer services
Transport 2000 claims both First Great Western (FGW) and Thames Trains admitted the measure would be introduced, at a private meeting last week.
The lobby group said the details have not been made public, but the companies would take the action because FGW is more than 40 drivers short.
Both train companies denied the claim, but FGW admitted a number of options were being considered.
Driver shortage
David Redgewell, south west spokesman for Transport 2000, said the move was revealed at a confidential stakeholder meeting involving various railway bodies last Thursday.
"The reason Oxford is being cut back is they are short of drivers, they are 41 drivers short at Oxford," he said.
"They are drawing up an emergency timetable on the Oxford line.
"Occasionally the service is late or cancelled. After Christmas they are going on an emergency timetable, the details of which we don't know.
"We are unhappy because at the moment the number of services is enough to persuade you to leave the car at home.
"If it is reduced it's not an alternative to the car."
Elaine Wilde, a spokeswoman for FGW said: "Bristol-Oxford is a joint venture with Thames Trains.
"There have been difficulties, Thames Trains have admitted there have been difficulties."
"There is no change at the moment."
Options considered
Asked whether an emergency timetable was being drawn up she said: "We are considering a number of options."
Jonathan Radley, spokesman for Thames Trains said: "This is pure speculation by Transport 2000.
"They are putting two and two together and making seven.
"No decision has yet been made about this service and when there is we will announce it, we're not backward about coming forward."
New trains
In July, the FGW unveiled an £80m fleet of new passenger trains at a ceremony in Bristol.
They have been built to run between Bristol and London.
But the introduction of the trains has been delayed by a year due to technical problems.
The company said the new trains would allow more frequent services and would lead to dramatic improvements in performance.