The cars' owners are part of a delegation from Tavistock's twin town of Celle — the party recently contacted town clerk Roger Howard to request permission to use the square during their visit in May.
During a heated debate last Tuesday, Col Howard reminded members that council policy was not to allow cars on the square 'come hell or high water' — unless they were an integral part of a proper display.
Former mayor Cllr Jenny Metcalf said: 'This would be so contentious, it would cause a vast furore, it would be a red rag to a bull.
'I think the Guildhall Car Park would be much more practical — and less contentious.'
Cllr Anne Johnson agreed with Cllr Metcalf. She said many local groups and organisations in the past had been refused permission to use Bedford Square for vehicles.
'We have our rules and regulations — are we changing them because we think it would look nice?' she said.
Cllr Mandy Govier pointed out that if the cars used Bedford Square on a trading day, it would cost the council in terms of manpower in seeing them safely on and off the paved area.
But Cllr John Sellis said it was 'absolutely ridiculous' not to allow the German cars to use the square.
He said: 'They are our guests for goodness sake. If we close the Guildhall Car Park we will have to close it for the day, when they may only be there for two hours. I think using the square would be ideal.'
Cllr David Whitcomb said considering Tavistock was twinned with Celle, he felt the German cars should be allowed to use the square. 'I am all for it,' he said.
Cllr David Best proposed the German visitors should be allowed to park on Bedford Square 'as a special concession' — the proposal was carried by six votes to five with one abstention.
An amendment proposed by Cllr Harry Smith to recoup any costs incurred — which the German contingent had already offered to pay — was turned down.
Bedford Square was paved over in 1999 as part of a controversial enhancement project, reducing the number of lanes of traffic through the town centre and doing away with coaches and cars parked in front of the historic town hall.
Technically, the area is part of Devon's highway system, but the town council manages its use on behalf of the county.
Former town councillors have been vociferous over what the paved area should — or should not — be used for, particularly when vehicles have been involved.
Tavistock Lions Club held a successful car show on the square for several years as part of the town's annual carnival, which raised substantial sums for charity. However, the council rescinded the club's licence to hold the event in 2004 as it was felt the show was not an appropriate use of the square.
And a booking by a local Capri owners' club later the same year, prompted calls for clarity over the council's policy, when members were told to 'get their act together and play by the rules'.
Thirty members of the Friends of Wiessmannfreunde will be bringing their cars, which resemble a cross between a Morgan and an E-Type Jaguar, to Tavistock on May 21. The group will have lunch in Tavistock — they are staying at Bovey Castle.