Hi Vitruvius,Certainly sounds like the Morgan shuffle.Had this on my car when I bought it, used to occur around 45 MPH .Have since fitted new kingpins and bushes which has completely cured the problem.Check for movement in each wheel by jacking up the car one wheel at a time . Check by lifting the wheel from the bottom upwards and outwards,the ideal would not to feel any free play here.
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Regards Barry 78 4/4 4 Seater