On Monday, jams are anticipated on the A303 around Stonehenge in Wiltshire, and on the M5 between Bristol and Taunton.
“Our research shows it could be one of the busiest Christmas getaways that we’ve seen in years,” Mr Dennis said.
He added that Christmas Eve would also be hectic, with “lots of people making last-minute trips to see friends and family”.
To avoid the worst of the jams, drivers were advised to tune into local radio stations and refer to traffic apps before setting out.
Great Western Railway has issued warnings advising people not to travel by train to Bath on Sunday.
More optimistically, the Met Office has said conditions for drivers will not be too bad over Christmas, with temperatures well above freezing, although wind and rain is expected.
Christmas Day, Boxing Day and New Year’s Day are expected to be the quietest days on the roads.