Problem with polybushes is that they basically don't cope with roll or its asymmetrical cousins twist and skew.
P38 has pure leading and trailing link suspension with solid axles. Calling the front links radius arms is just a different name.
Consider replacing all the bushes with solid pins in metal bearings. Suspension will go up and down OK but it can't roll, twist or skew without staring things. Not even with rose joints at the arm to body connection. The rubber bushes provide the flexibility to allow such movement. The long links mean that the axles have to divine their connection to the car at considerable distance but do allow the body to float along fairly independently relative to axles and minimise the twisting movements in the bushes. The long, rubber bushed links means the inherent transverse location between car and axles is very poor. Hence the Panhard Rod links front and back which tie the axles to the car from side to side.
Panhard Rod links tie things together side to side pretty well but the geometry is inherently infelicitous and pure rotation at the bush is impossible. The longer the link the less the angles involved but either the pin has to shift away from central within the bush or the rod itself needs to distort. Polybushes do have tiny bit of inherent flexibility but its far less than rubber. Only reason you can get away with them is the sheer length of the arms which minimise the the angles involved. It doesn't begin to work as designed but at least the bushes don't tear out in nothing flat. At the front the Panhard rod ones are most seriously overloaded and will fail first. I'd be unsurprised to discover that the bushes actually wear sloppy quite quickly so things can wobble around enough to cope with geometric variations but not so much that the steering can't cope. Behaviour of the compress to fit axle front mounting bushes is interesting as it stops the sort of horrid front end behaviour associated with old fashioned leaf sprung dead axle cars. Imagine P38 on a Series Land Rover suspension set up. Yikes! maybe not.
Not quite so bad at the back because the trailing link has some inherent flexibility to help reduce strain on the bushes. No direct steering loads either.
When you get down to it the whole Range Rover suspension arrangement is a very clever and sophisticated design despite its apparent simplicity. Polybushes are nearly as bad as coil springs for mucking up suspension really. Pressing on in a coil sprung, polybushed P38 with uprated dampers is probably an "interesting" experience.
The whole polybush thing comes from track racing where cars are set up with hard suspension to minimise movement and, especially, roll. No issues with geometrically proper systems like double wishbones, watt linkages et al which work fine with solid pins and rose joints anyway but the minor compliance of polys makes assembly easier. But when you come to saloon cars and less geometrically correct systems the inevitable compliance of rubber works agains the rock hard suspension set-up hence polybushes do have real advantages.
Clive