71 Dodge Dart Swinger in England

Looks great. You should also ditch that rubber fuel line and bend some steel lines.

I think you mentioned that the engine was a 360. The balancer outer could have slipped on the rubber and is out of balance. 360s are externally balanced. The outer balance weight ring has some metal missing from it in order to help with the external balance. If the outer ring has slipped then that may be a cause of vibration.

A second cause could be a torque converter in the car from a 318 without an external balance weight. I think B&M makes a flexplate that allows you to use a neutral balance torque converter (no weight) on a 360 as the B&M flexplate is set up as an external balance flexplate.